Embodiments of this invention relate to a processing chamber and methods of distributing reactants therein to facilitate cyclical layer deposition of films on a substrate. One embodiment of a substrate processing chamber includes a chamber body and a substrate support disposed in the chamber body. A lid is disposed on the chamber body. An injection plate having a recess is mounted on the lid. A bottom surface of the recess has a plurality of apertures limited to an area proximate a central portion of the substrate receiving surface of the substrate support. Another embodiment of a substrate processing chamber includes a chamber body having interior sidewalls and an interior bottom wall. A top liner is disposed along the interior sidewalls of the chamber body. A bottom liner is disposed on the interior bottom wall of the chamber body. A gap is defined between the top liner and the bottom liner to allow a purge gas to be introduced therethrough. Still another embodiment of a substrate processing chamber includes a chamber body and a lid assembly defining an interior cavity. Two or more exhausts are selectively coupled to the interior cavity.
Additionally, this application is related to U.S. patent application Ser. No. 09/798,251, entitled "Lid Assembly for a Processing System to Facilitate Sequential Deposition Techniques" filed on Mar. 2, 2001; U.S. patent application Ser. No. 09/798,258, entitled "Processing Chamber and Method of Distributing Process Fluids Therein to Facilitate Sequential Deposition of Films" filed on Mar. 2, 2001; U.S. patent application Ser. No. 09/605,593, entitled "Bifurcated Deposition Process For Depositing Refractory Metal Layer Employing Atomic Layer Deposition And Chemical Vapor Deposition" filed on Jun. 28, 2000; and U.S. patent application Ser. No. 09/678,266, entitled "Methods and Apparatus For Depositing Refractory Metal Layers Employing Sequential Deposition Techniques To Form Nucleation Layers" filed on Oct. 3, 2000, all of which are incorporated herein by reference in their entireties.
One embodiment of a method for forming aluminum oxide over a substrate includes providing one or more cycles of compounds to a region adjacent a substrate surface. Each cycle includes separately providing a pulse of an aluminum precursor and a pulse of an oxidizing agent to a region adjacent a substrate surface. Each cycle further includes providing a purge gas to the region adjacent the substrate surface between the pulse of the aluminum precursor and the pulse of the oxidizing agent.
FIG. 19 is a flow chart depicting various embodiments of a deposition of aluminum oxide (Al xOy) using controllable/variable hydrogen/oxygen content water vapor.
FIG. 1 is a schematic cross-sectional view of one exemplary embodiment of a processing chamber  10 that may be used to deposit aluminum oxide by cyclical deposition techniques in accordance with aspects of the present invention. The term "cyclical deposition" as used herein refers to the sequential introduction of reactants to deposit a thin layer over a structure and includes processing techniques such as atomic layer deposition and rapid sequential chemical vapor deposition. Reactants can be precursors, reducing agents, oxidizing agents, catalysts, atomic species, other compounds, and mixtures thereof. The sequential introduction of reactants may be repeated to deposit a plurality of thin layers to form a conformal layer to a desired thickness. More than one of the reactants may be present in the chamber at the same time during the sequential introduction of reactants. Alternatively, only one of the reactants may be present in the chamber at one time during the sequential introduction of reactants. The present invention also includes depositing aluminum oxide by cyclical deposition techniques utilizing other processing systems.
The processing chamber  10 includes a chamber body 14 and a lid assembly 20. The chamber body 14 includes a slit valve opening 44 to allow transfer of a substrate to and from the processing chamber 10. Disposed within the processing chamber 10 is a heater/lift assembly 46 that includes a substrate support pedestal 48. The heater/lift assembly 46 may be moved vertically within the chamber 10 so that a distance between the support pedestal 48 and the lid assembly 20 may be controlled. The support pedestal 48 may include an embedded heater element, such as a resistive heater element or heat transfer fluid, utilized to control the temperature thereof. Optionally, a substrate disposed on the support pedestal 48 may be heated using radiant heat. The support pedestal 48 may also be configured to hold a substrate thereon, such as by a vacuum chuck, by an electrostatic chuck, or by a clamp ring.
The lid assembly  20 includes a lid 21 and an injection plate 36. The injection plate 36 is generally annular and includes a side facing the lid 21 and another side generally facing the support pedestal 48. The lid 21 includes one or more inlet passages 86 disposed therethrough to allow delivery of reactive (i.e. precursor, reductant, oxidant), carrier, purge, cleaning and/or other fluids through the lid 21 and into the processing chamber 10. Fluids enter a plenum or region 88 defined between the lid 21 and the injection plate 36 before entering the processing chamber 10. The injection plate 36 may include a mixing lip 84 to re-direct gases toward the center of the plenum 88 and into the process chamber 10. The injection plate 36 is utilized to prevent gases delivered into the chamber 10 from blowing off gases adsorbed onto the surface of the substrate. The injection plate 36 may be removed from the lid 21 for cleaning and/or replacement. Alternatively, the injection plate 36 and lid 21 may be fabricated as a single member.
FIG. 2 is a schematic top perspective view and FIG. 3 is a schematic cross-sectional view of the injection plate  36 of FIG. 1. The injection plate 36 has a passage 700 formed therethrough. A recess 702, typically concentric with the passage 700, and the lid 21 define the plenum 88 (FIG. 1) therebetween. The recess 702, typically circular in form, is configured to extend radially from a centerline of the injection plate 36 to a diameter that extends to or beyond the one or more inlet passages 86 (FIG. 1) disposed through the lid 21 so that gases flowing from the inlet passages 86 enter the recess 702 and exit through the passage 700.
A bottom  712 of the recess 702 defines the mixing lip 84 that extends radially inward to the passage 700. Gases flowing into the recess 702 from the inlet passages 86 are re-directed by the surface of the mixing lip 84 generally towards the center of the recess 702 before passing through the passage 700 and into the process chamber 10. The recess 702 combined with a singular exit passage for delivering gases to the chamber 10 (e.g., the passage 700) advantageously reduces the surface area and orifices requiring purging and cleaning over conventional showerheads having multiple orifices for gas delivery.
The side of the injection plate  36 facing the lid 21 may include features for reducing the contact area between the injection plate 36 and the lid 21. Providing reduced contact area allows the injection plate 36 to be operated at a higher temperature than the lid 21, which in some processes enhances deposition performance. As shown in FIGS. 2 and 3, the side of the injection plate 36 facing the lid 21 may include a plurality of bosses 706, each having a mounting hole 707 passing therethrough. The bosses 706 allow the injection plate 36 to be coupled to the lid 21 by fasteners passing through the mounting holes 707 into holes formed in the lid 21. Additionally, a ring 708 projects from the side of the injection plate 36 facing the lid 21 and circumscribes the recess 702. The ring 708 and bosses 706 project to a common elevation that allows the injection plate 36 to be coupled to the lid 21 in a spaced-apart relation. The spaced-apart relation and the controlled contact area permit a controlled thermal transfer between the injection plate 36 and the lid 21. Accordingly, the contact area provided by bosses 706 and the ring 708 may be designed to tailor the amount and location of the solid-to-solid contact area available for thermal transfer between the injection plate 36 and the lid 21 as a particular deposition process requires.
FIG. 4 is a schematic top perspective view and FIG. 5 is a schematic cross-sectional view of another embodiment of an injection plate  36′. A recess 722 and the lid 21 define a plenum 788 therebetween. A bottom 732 of the recess 722 defines a surface have a plurality of apertures 720. The apertures 720 are formed in the injection plate 36 so that when the injection plate 36 is disposed above a substrate support the apertures 720 are proximate a central portion of the substrate receiving surface of the substrate support. The recess 722, typically circular in form, is configured to extend radially from a centerline of the injection plate 36 to a diameter that extends to or beyond the one or more inlet passages 86 (FIG. 1) disposed through the lid 21 so that gases flowing from the inlet passages 86 enter the recess 722 and exit through the apertures 720. Gases flowing into the recess 722 from the inlet passages 86 are re-directed by the surface of the bottom 732 of the recess 722, and then, pass through apertures 720 and into the process chamber 10. In one aspect, the apertures 720 provide gases proximate a central portion of the substrate support which reduces the surface area requiring purging and cleaning over conventional showerheads having multiple orifices positioned above substantially the entire surface of the substrate receiving surface of a substrate support.
The side of the injection plate  36′ facing the lid 21 may include features for reducing the contact area between the injection plate 36′ and the lid 21. Providing reduced contact area allows the injection plate 36′ to be operated at a higher temperature than the lid 21, which in some processes enhances deposition performance. As shown in FIGS. 4 and 5, the side of the injection plate 36′ facing the lid 21 may include a plurality of bosses 726, each having a mounting hole 727 passing therethrough. The bosses 726 allow the injection plate 36 to be coupled to the lid 21 by fasteners passing through the mounting holes 727 into holes formed in the lid 21. Additionally, a ring 728 projects from the side of the injection plate 36′ facing the lid 21 and circumscribes the recess 722. The ring 728 and bosses 726 project to a common elevation that allows the injection plate 36′ to be coupled to the lid 21 in a spaced-apart relation. The spaced-apart relation and the controlled contact area permit a controlled thermal transfer between the injection plate 36′ and the lid 21. Accordingly, the contact area provided by bosses 726 and the ring 728 may be designed to tailor the amount and location of the solid-to-solid contact area available for thermal transfer between the injection plate 36′ and the lid 21 as a particular deposition process requires.
Referring to FIG. 1, the lid  21 may further comprise one or more temperature fluid control channels 29 to control the temperature of the lid assembly 20 by providing a cooling fluid or a heating fluid to the lid 21 depending on the particular process being performed in the chamber 10. Controlling the temperature of the lid assembly 20 may be used to prevent gas decomposition, deposition, or condensation thereon.
Disposed along the sidewalls of the chamber body  14 proximate the lid assembly 20 is a mouth of a pumping channel 62. The pumping channel 62 is coupled by a conduit 66 to a pump system 18 which controls the pressure of the processing chamber 10. A pumping plate 26 may be optionally disposed over the mouth of the pumping channel 62. The pumping plate 26 includes a plurality of apertures 27 formed therethrough to control the flow of fluids from the processing chamber 10 into the pumping channel 62. In other embodiments, the pumping plate 26 may be removed to increase conductance into the pumping channel 62.
In the figure, the pump system  18 comprises a dual exhaust system having a first exhaust 18A and a second exhaust 18B. Each exhaust may be selectively coupled to the interior cavity of the chamber body 14. For example, at any given moment, either one, both, or none of the exhausts 18A, 18B are open to the interior cavity of the chamber. The dual exhaust system is described in greater detail below in reference to FIGS. 17 and 18.
Still referring to FIG. 1, a liner assembly is disposed in the processing chamber  10 and includes a top liner 54 and a bottom liner 56. The top liner 54 and the bottom liner 56 may be formed from quartz or any suitable material such as aluminum, stainless steal, graphite, silicon carbide, ceramics, aluminum oxide, aluminum nitride, and other suitable materials. The top liner 54 surrounds the support pedestal 48 and includes an aperture 60 that aligns with the slit valve opening 44 disposed on a sidewall of the chamber body 14.
The bottom liner  56 extends transversely to the top liner 54 and is disposed against a bottom of the chamber body 14 disposed opposite to the lid assembly 20. A chamber channel 58 is defined between the chamber body 14 and the bottom liner 56. A purge gas is introduced from a purge gas inlet 51 into the chamber channel 58 and flows through gap 664 between the bottom liner 56 and the top liner 54. The purge gas flows between the top liner 56 and the substrate support pedestal 48 to confine process gases in a volume between the substrate support pedestal 48 and the lid assembly 20. As a consequence, pulse times of precursors gases and purging of this volume for a particular process may be reduced.
FIG. 6 is a schematic perspective assembly view of the top liner  54 and the bottom liner 56. The bottom liner 56 includes an orifice 650 to allow lift ring 78 a (FIG. 1) and the stem of the 46 heater/lift assembly (FIG. 1) to be disposed therethrough. The bottom liner further includes a plurality of ledges 662 for supporting the top liner 54. The top liner 54 rests on the ledges 662 so that a there is a gap 664 (FIG. 1) between the top liner 54 and the bottom liner 56 for the flow of a purge gas therethrough from the chamber channel 58. The top liner 54 has a pair of extending fingers 670 which align around one of the ledges 662 for alignment of the top liner 54 within the processing chamber 10.
FIG. 7 is a schematic perspective view of one embodiment of the processing chamber  10. The lid assembly 20 is pivotally coupled to the chamber body 14 via hinges 22. A handle 24 is attached to the lid assembly 20 opposite the hinges 22. The handle 24 facilitates moving the lid assembly 20 between opened and closed positions. In the opened position, the interior of the chamber body 14 is exposed. In the closed position shown in FIG. 1, the vacuum lid assembly 20 covers the chamber body 14 forming a fluid-tight seal therewith. In this manner, a vacuum formed in the processing chamber 10 is maintained as the lid assembly 20 seals against the chamber body 14.
A process fluid injection assembly  30 is mounted to the lid assembly 20 to deliver reactive, carrier, purge, cleaning and/or other fluids into the processing chamber 10. The fluid injection assembly 30 includes a gas manifold 34 mounting a plurality of control valves, 32 a, 32 b and 32 c. The valves 32 a, 32 b and 32 c provide rapid and precise gas flow with valve open and close cycles of less than about one second, e.g., less than about 0.1 second. In one embodiment, the valves 32 a, 32 b and 32 c are surface mounted, electronically actuated valves. One valve that may be utilized is available from Fujikin of Japan as part number FR-21-6.35 UGF-APD. In another embodiment, the valves 32 a, 32 b, and 32 c are surface mounted, pneumatically actuated valves. Other valves that operate at substantially the same speed and precision may also be used. In one embodiment, an aluminum-containing compound, such as trimethyl aluminum Al(CH3)3, is connected to valve 32 a and an oxidizing compound, such as ozone O3, is connected to valve 32 c.
The lid assembly  20 may further optionally include one or more (two are shown in FIG. 7) gas reservoirs 33, 35 that are fluidly connected between one or more process gas sources and the gas manifold 34. The gas reservoirs 33, 35 provide bulk gas delivery proximate to each of the valves 32 a, 32 b, 32 c. The reservoirs 33,35 are sized to insure that an adequate gas volume is available proximate to the valves 32 a, 32 b, 32 c during each cycle of the valves 32 a, 32 b and 32 c during processing to minimize the time required for fluid delivery, thereby shortening sequential deposition cycles. For example, the reservoirs 33, 35 may be about 5 times the volume required in each gas delivery cycle.
Gas lines  37, 39 extend between the connectors 41, 43 and the reservoirs 33, 35 respectively. The connectors 41, 43 are coupled to the lid 21. The process gases are typically delivered through the chamber body 14 through the lid assembly 20, and to the process fluid injection assembly 30.
To maximize the throughput, the lid assembly  20 and the injection assembly 30 are configured to minimize the time required to inject process fluids into the processing chamber 10 and disperse the fluids over the process region proximate to the support pedestal 48. For example, the proximity of the reservoirs 33, 35 and valves 32 a-b to the gas manifold 34 reduce the response times of fluid delivery, thereby enhancing the frequency of pulses utilized in ALD deposition processes.
Additional connectors  45, 47 are mounted adjacent the gas manifold 34 down stream from the reservoirs 33, 35 and connect to the reservoirs 33, 35 by gas lines 49, 51. The connectors 45, 47 and gas lines 49, 51 generally provide a flowpath for process gases from the reservoirs 33, 35 to the gas manifold 34. A purge gas line 53 is similarly connected between a connector 55 and a connection 57 on the gas manifold 34.
FIG. 8 is a schematic partial perspective view of the lid assembly  20 and the process fluid injection assembly 30. The gas manifold 34 includes a body defining a plurality of mounting surfaces 59, 61, 64. Each valve 32 is fluidly coupled to a separate set of gas channels of the gas manifold 34. Valve 32 a is coupled to gas channels 69 a, 69 b. Valve 32 b is coupled to gas channels 67 a, 67 b. Gas channels 69 a, 67 a provides passage of gases through the gas manifold 34 to the respective valves 32 a, 32 b. Gas channels 69 b, 67 b delivers gases from the respective valves 32 a, 32 b through the gas manifold 34 and into a respective inlet passage 86 disposed through the lid 21, through the plenum 88, and into the processing chamber. The gas manifold 34 and the valves 32 may be optionally heated to control the temperature of gases flowing therethrough.
The fluid injection assembly  30 may further include an oxidizing agent delivery device 65. The oxidizing agent delivery device 65 may be coupled to a valve 32 or reservoir of the fluid injection assembly 30 or may be coupled to a gas channel through the gas manifold 34. The oxidizing agent delivery device 65 may be an ozonator if ozone processing is desired or a remote activation device if other oxidizing gases are desired. Exemplary ozonators are available from Applied Science and Technology, Inc., of Woburn, Mass.
In another embodiment, oxidizing agent delivery device  65 may be a remote activation source, such as a remote plasma generator, used to generate a plasma of reactive species which can be delivered into the chamber 10. The plasma of reactive species may be generated by applying an electric field to a compound within the remote activation source. The reactive species are then introduced into the chamber 10 via the lid assembly 20. Any power source that is capable of activating the intended compounds may be used. For example, power sources using DC, radio frequency (e), and microwave (MW) based discharge techniques may be used. If an RF power source is used, it can be either capacitively or inductively coupled. The activation may also be generated by a thermally based technique, a gas breakdown technique, a high intensity light source (e.g., UV energy), or exposure to an x-ray source. Exemplary remote plasma sources are available from vendors such as MKS Instruments, Inc. and Advanced Energy Industries, Inc.
In the embodiment shown in FIG. 8, the oxidizing agent delivery device  65 is mounted on an upper surface of the lid assembly 20 so that the reactive oxidizing agent may be delivered in a minimized conductance pathway. It is believed that mounting the oxidizing agent delivery device 65 on the lid assembly provides an oxidizing agent, such as ozone or oxygen species, at a higher concentration and reactivity than delivering oxidizing agents using conventional techniques and methods. In other embodiments, the oxidizing agent delivery device 65 may be situated apart from the lid assembly 20 but in close proximity to the processing chamber 10 so that a minimized or low conductance pathway is created to improve delivery of the oxidizing agent. In another embodiment, the oxidizing agent delivery device 65 may be located in the pump alley and plumbed to the gas cabinet 2250 (shown in FIG. 9).
In other embodiments, a remote plasma showerhead may be used to generate a plasma. One example of a remote plasma showerhead is disclosed in U.S. patent application Ser. No. 10/197,940 filed Jul. 16, 2002, which claims priority to U.S. Provisional Patent Application Serial No. 60/352,191 filed Jan. 26, 2002, both of which are incorporated by reference to the extent not inconsistent with the present disclosure. FIG. 20 is a schematic cross-section view of an example of a processing chamber having a remote plasma showerhead  2130. The remote plasma showerhead 2030 comprises a top shower plate 2160 and a bottom shower plate 2170. A power source 2190 is coupled to the top shower plate 160 to provide a power electrode and the bottom shower plate 2170 is grounded to provide a ground electrode. The power source 2190 may be an RF or DC power source. An electric field may be established between the top shower plate 2160 and the bottom shower plate 2170 to generate a plasma from the gases introduced between the top shower plate 2160 and the bottom shower plate 2170.
FIG. 9 is a schematic diagram illustrating the components of an aluminum oxide deposition system  2200 in accordance with an embodiment of the present invention. The aluminum oxide deposition system 2200 includes an oxidizing agent delivery device 2210 coupled to a gas source 2240 and/or to a gas cabinet 2250 to provide one or more oxidizing agents thereto. A chiller 2220 may be coupled to the oxidizing agent delivery device 2210 to cool the oxidizing agent delivery device 2210. The gas source 2240 is coupled to the gas cabinet 2250 which in turn is coupled to a processing chamber 10 to provide a plurality of gases thereto. A heater 2230 may be coupled to a lid assembly 20 of the processing chamber 10 to heat the lid assembly 20. A pump system 18 is coupled to the processing chamber 10 to provide a vacuum to the processing chamber 10. A control system 70 may be coupled to the components of the system 2200 to provide control signals thereto.
The oxidizing agent delivery device  2210 may deliver gases, such as, O2 and N2, to the gas source 2240. The oxidizing agent delivery device 2210 is also connected to the gas cabinet 2250 to directly deliver an oxidizing agent, e.g., O3 or oxygen radicals, to the gas cabinet 2250. The gas source 2240, which delivers gases, such as, argon, helium and nitrogen, is connected to the gas cabinet 2250. The gas cabinet 2250 also includes an ampoule containing a liquid aluminum precursor and a vapor injection system. The ampoule, the line delivering the precursor to the vaporizer, the vaporizer, and the line carrying the vaporized precursor to the chamber can each be heated using conventional methods of heating to reduce the viscosity of the metal-containing compound; to assist in the vaporization of the liquid material prior to injection into the lid assembly 20; and to ensure that the vaporized aluminum precursor does not condense. The heating system is controllable to maintain the lines in a temperature range-determined by the particular aluminum precursor used so that the vapor does not condense nor is it heated to such a temperature that the precursor begins to decompose. Alternatively, the metal-containing compound may be pre-mixed with a solvent to reduce its viscosity and then vaporized prior to flow into the injection valves leading into the chamber. A carrier gas, such as argon, helium, hydrogen, nitrogen, and combinations/mixtures thereof, may be used within the vapor injection system to help facilitate the flow of the metal-containing compound into the lid assembly 20.
A controller  70 regulates the operations of the various components of system 2200. The controller 70 includes a processor 72 in data communication with memory, such as random access memory 74 and a hard disk drive 76 and is in communication with at least the pump system 18 (FIG. 1) and the valves 32 a, 32 b and 32 c (FIG. 7).
The system  2200 may further include a diverter 2290 coupled between the gas cabinet 2250 and the chamber 10. The diverter is selectively movable between a first position and a second position. In the first position, the diverter 2290 directs a gas or gases from the gas cabinet 2250 to the chamber 10. In the second position, the diverter 2290 directs a gas or gas mixture from the gas cabinet 2250 to the foreline of the pump system 18. In one aspect, the diverter 2290 helps reduce the pressure variations of the pump system 18. As shown in the figure, the diverter is coupled to the oxidizing agent line. In other embodiments, the diverter may be coupled to other reactant lines. The diverter 2290 is discussed in more detail in reference to FIG. 18.
FIG. 10 is a schematic top plan view of an integrated processing system  1000 configured to form a film stack having an aluminum oxide layer in accordance with embodiments of the present invention. The apparatus is a Centura® system and is commercially available from Applied Materials, Inc. of Santa Clara, Calif. The particular embodiment of the system 1000 is provided to illustrate the invention and should not be used to limit the scope of the invention unless otherwise set forth in the claims.
The system  1000 generally includes load lock chambers 1022 for the transfer of substrates into and out from the system 1000. Typically, since the system 1000 is under vacuum, the load lock chambers 1022 may "pump down" the substrates introduced into the system 1000. A robot 1030 having a blade 1034 may transfer the substrates between the load lock chambers 1022 and processing chambers 1010, 1012, 1014, 1016, 1020. Any of the processing chambers 1010, 1012, 1014, 1016, 1020 may be removed from the system 1000 if not necessary for the particular process to be performed by the system 1000. Optionally, a factory interface may be connected on the front end of the system 1000 and may include one or more metrology chambers 1018 connected thereto.
One or more of the chambers  1010, 1012, 1014, 1016, 1020 is an aluminum oxide chamber, such as a processing chamber 10 described above in reference to FIGS. 1-9. Optionally, one or more of the chambers 1010, 1012, 1014, 1016, 1020 may be adapted to deposit a dielectric material, a conductive material, or another material. Optionally, one or more of the chambers 1010, 1012, 1014, 1016, 1020 may be a cleaning chamber, such as a conventional dry chemistry cleaning chamber. Cleaning chambers are used to remove any unwanted products on a substrate following previous processes and prior to additional processing. Examples of a conventional dry chemistry chamber include a Preclean II chamber available from Applied Materials, Inc. of Santa Clara, Calif. Exemplary dry chemistry systems include, but are not limited to, dry plasma systems having controlled environments therein. Suitable dry clean processes include plasma processes of reactive chemistries, such as, fluorine, oxygen, hydrogen, and any combination of inert gases, such as, argon or other sputtering gases. The dry cleaning chambers may generate the plasma in situ or in a remote plasma source connected thereto. Optionally, one or more of the chambers 1010, 1012, 1014,1016,1020 may be an anneal chamber or other thermal processing chamber, such as a Radiance Centura chamber available from Applied Materials, Inc. of Santa Clara, Calif. The system 1000 may also include other types of processing chambers.
One example of a possible configuration of the integrated processing system  1000 includes a load lock chamber 1022 adapted to provide de-gas or pre-heat the substrate, an aluminum oxide cyclical deposition chamber 1010, a second dielectric deposition chamber 1012, a metal deposition chamber 1014, a third dielectric deposition chamber 1016, and an anneal chamber 1020. The substrate passes through the various processing chamber to fabricate a substrate ready for resist deposition and patterning. Of course, other configurations of integrated processing system 1000 are possible.
FIG. 11 is a flow chart depicting various embodiments of a method for depositing an aluminum oxide layer by cyclical layer deposition onto a substrate in a processing chamber, such processing chamber  10 described above in reference to FIGS. 1-9. The method generally begins with positioning a substrate on a substrate support member in the chamber. With the substrate positioned on the substrate support member, in step 1101, the aluminum oxide deposition process begins with the introduction of an aluminum precursor, such as trimethylaluminum, through the lid assembly into the chamber proximate the substrate surface. Other aluminum precursors may also be used such as dimethylaluminumhydride, triisopropoxyaluminum, other aluminum precursors of the formula Al(R1)(R2)(R3) in which R1, R2, R3 are the same or different ligands, and other suitable aluminum precursors. Once the aluminum precursor is introduced into the chamber 10, the method continues to a purge step 1102, where a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. Examples of purge gases which may be used include, but are not limited to, helium (He), argon (Ar), nitrogen (N2), hydrogen (H2), and mixtures thereof. Then in step 1103, an oxidizing agent, such as ozone or oxygen species, is introduced through the lid assembly into the chamber. Other oxidizing agents may also be used, such as H2O, N2O, NO and other suitable oxidizing agents. The oxidizing agent is generally introduced into the chamber in a manner that directs the oxidizing agent toward the surface of the substrate, and as such, the oxidizing agent reacts with the aluminum precursor to facilitate the formation of an aluminum oxide layer on the substrate.
Once the oxidizing agent has been introduced through the lid assembly into the chamber, the method continues to step  1104, where another purge gas may be introduced into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. The deposition cycle can continue back to the aluminum precursor pulse if it is determined at step 1105 that additional film thickness is desired. The aluminum oxide deposition cycle can be terminated if the desired film thickness is deposited as indicated at step 1106. If additional films are to be deposited as determined at step 1107, the substrate begins undergoing such processing at step 1108. The method of depositing aluminum oxide has been depicted as starting with a pulse of an aluminum precursor. In other embodiments, the aluminum oxide deposition may begin with a pulse of an oxidizing agent.
FIG. 12 is a flow chart depicting various embodiments of a method for annealing sequences performed at various times during the aluminum oxide deposition cycle in a processing chamber, such as processing chamber  10 described above in reference to FIGS. 1-9. In step 1201, a pulse of an aluminum precursor is introduced through the lid assembly into the chamber proximate the substrate surface. In step 1202, a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. In step 1203, an oxidizing agent is introduced through the lid assembly into the chamber. In step 1204, a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. If a desired thickness of the aluminum oxide layer has not been reached, an anneal step 1212 may be performed. Then, the cycle of pulses of aluminum precursor and oxidizing agent continues in steps 1201-1204. As a consequence, an annealing step may be performed after every deposition cycle, or after any number of cycles are performed. As an example, an annealing step may be performed every third cycle, every four cycle, etc. or at a midpoint during the deposition process. After a desired thickness of an aluminum oxide layer has been reached, a post-anneal 1222 may be performed. If other processes are to be performed, then the substrate may be transferred to other processing chambers.
FIG. 13 is a flow diagram depicting various embodiments of a method for additional oxidizing sequences which may be performed at various times during the aluminum oxide deposition cycle in a processing chamber, such as processing chamber  10 as described above in reference to FIGS. 1-9. In step 1301, a pulse of an aluminum precursor is introduced through the lid assembly into the chamber proximate the substrate surface. In step 1302, a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. In step 1303, an oxidizing agent is introduced through the lid assembly into the chamber. If a prolonged oxidation is desired, then the oxidizing agent continues into the chamber in step 1312. Then in step 1304, a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. If a desired thickness of the aluminum oxide layer has not been reached, the cycle of pulses of aluminum precursor and oxidizing agent continues. The additional oxidizing sequence 1312 may be performed during every deposition cycle, or during any number of deposition cycles. As an example, the additional oxidizing sequence 1312 may be performed during every cycle, every third cycle, every fourth cycle, etc. or at the midpoint during the deposition process. In other embodiments, the prolonged oxidation process may also be used as a pre-treatment step or a post-treatment step in situ.
FIG. 14 is a flow diagram depicting an integrated deposition sequence of a controllable, variable dielectric constant laminate which may be performed in an integrated process system, such as processing system  1000 described in reference to FIG. 10. In step 1401, an aluminum oxide layer is first deposited. In step 1402, a second layer having a dielectric constant k2 is deposited thereover. In step 1403, a third layer having a dielectric constant k3 is deposited over the second dielectric constant layer. Between each step an anneal step can be performed as necessary to form a film having a desired composition and dielectric constant. In one embodiment, the sequence is preceded by a preclean and/or pretreatment process prior to deposition of materials, e.g., the aluminum oxide deposition. In performing the overall process sequence, aluminum oxide may be deposited using multiple cycles until a desired thickness is reached.
FIG. 15 is a flow diagram depicting another embodiment of an integrated sequence to form a controllable, variable dielectric constant laminate which may be performed in an integrated process system, such as processing system  1000 described in reference to FIG. 10. In step 1501, an aluminum oxide layer is first deposited. In step 1502, a second layer having a dielectric constant k2 is deposited thereover. In step 1503, a third layer having a dielectric constant k3 is deposited over the second dielectric constant layer. If a desired thickness of the laminate is achieved in a single cycle deposition, the process may be ended. However, if a desired thickness of the laminate is not achieved, then another deposition cycle of each of the layers may be subsequently performed over the first stack of layers. The deposition cycle of each layer may proceed until a desired thickness is formed. Following formation of the desired laminate film, the substrate can be exposed to additional processing.
The aluminum oxide deposition sequences as described in reference to FIGS.  11-15 may be followed by formation of materials thereover. For example, a metal, such as titanium, titanium nitride, tantalum, Ta nitride, tungsten, tungsten nitride, and other refractory metals or other suitable electrode materials may be deposited over the aluminum oxide layer or variable dielectric constant laminate layer. In addition, polysilicon, high dielectric constant materials, ferromagnetic materials, oxides, doped and undoped glass (USG, GPSG, PSG, PSG, etc.), carbon doped oxide films, silicon carbide, dielectric anti-reflective coatings, other films to prepare the structure for resistant deposition or patterning may be deposited, and other materials may be formed over the aluminum oxide layer or variable dielectric constant laminate layer.
FIG. 16 is a flow diagram depicting one example of an integrated process sequence for depositing dielectric and conductive materials which may be performed in an integrated process system, such as processing system  1000 described in reference to FIG. 10. In step 1601, an aluminum oxide film is deposited using a cyclical deposition process, such as the aluminum oxide deposition processes as described in reference to FIGS. 11-15. In step 1602, a metal top electrode is then formed thereover. In step 1603, a dielectric material, such as silicon oxide or a DARC layer, is then deposited on the top metal electrode. Following this sequence, the substrate is ready for resist deposition and patterning.
FIG. 17 is a diagram depicting one example of the control signals for delivering compounds in an aluminum oxide cyclical layer deposition method utilizing a process chamber having a dual exhaust system, such as processing chamber  10 as described above in reference to FIGS. 1-9. An aluminum precursor source 1702, such as a valve disposed on the fluid injection assembly 30 as described above in reference to FIGS. 7 and 8, provides a pulse 1704 of an aluminum precursor into the chamber. An aluminum precursor exhaust 1706, such as pump system 18A of FIG. 1, is in fluid communication with the chamber for a time period 1708. In general, the time period 1708 is longer than the duration of pulse 1704 of the aluminum precursor to ensure removal of the aluminum precursor from the chamber into the aluminum precursor exhaust 1706. An oxidizing agent source 1712, such as a valve disposed on the fluid injection assembly 30 as described above in reference to FIGS. 7 and 8, provides a pulse 1714 of an oxidizing agent. An oxidizing agent exhaust 1716, such as pump system 18A of FIG. 1, is in fluid communication with the chamber for a time period 1718. In general, the time period 1718 is longer than the duration of pulse 1714 of the oxidizing agent to ensure removal of the oxidizing agent from the chamber into the oxidizing agent exhaust 1716. In one aspect, utilizing separate exhausts for the aluminum precursor and the oxidizing agent reduces the likelihood of formation of particles within the pump system, and, therefore, extends the operating life of the pump system. In the figure, the time period 1708 of the aluminum precursor exhaust 1706 and the time period 1718 of the oxidizing agent exhaust 1716 in which the exhausts are open to the chamber are shown as overlapping. In other embodiments, the time periods in which the dual exhaust are open to the chamber do not overlap.
FIG. 18 is a diagram depicting one example of the control signals for delivering compounds in an aluminum oxide cyclical layer deposition method utilizing a process chamber having a dual exhaust system and a diverter, such as processing chamber  10 as described above in reference to FIGS. 1-9. An aluminum precursor source 1802, such as a valve disposed on the fluid injection assembly 30 as described above in reference to FIGS. 7 and 8, provides a pulse 1804 of an aluminum precursor into the chamber. An aluminum precursor exhaust 1806, such as pump system 18A of FIG. 1, is in fluid communication with the chamber for a time period 1808. In general, the time period 1808 is longer than the duration of pulse 1804 of the aluminum precursor to ensure removal of the aluminum precursor from the chamber into the aluminum precursor exhaust 1806. An oxidizing agent source 1812, such as gas cabinet 2250 as described above in reference to FIGS. 9, provides a continuous flow 1814 of an oxidizing agent. A diverter 1822, such as diverter 2290 of FIG. 9, diverts the oxidizing agent to the chamber for a time period 1824 and diverts the oxidizing agent to the foreline of the oxidizing agent exhaust 1816 for a time period 1826. An oxidizing agent exhaust 1816, such as pump system 18A of FIG. 1, is in fluid communication with the chamber for a time period 1818. In general, the time period 1818 is longer than the duration of the time period 1824 in which the oxidizing agent is diverted to the chamber to ensure removal of the oxidizing agent from the chamber into the oxidizing agent exhaust 1716. In one aspect, utilizing separate exhausts for the aluminum precursor and the oxidizing agent reduces the likelihood of formation of particles within the pump system, and, therefore, extends the operating life of the pump system. In another aspect, the diverter reduces pressure variations of the oxidizing agent exhaust 1816. In the figure, the time period 1808 of the aluminum precursor exhaust 1806 and the time period 1818 of the oxidizing agent exhaust 1816 in which the exhausts are open to the chamber are shown as overlapping. In other embodiments, the time periods in which the dual exhaust are open to the chamber do not overlap.
FIG. 19 is a flow chart depicting various embodiments of a deposition of aluminum oxide (Al xOy) using controllable/variable hydrogen/oxygen content water vapor with variable/selectable annealing and oxidizing sequences which may be performed in a single chamber or in a plurality of chambers. One example of a chamber adapted to provide a controllable/variable hydrogen/oxygen content water vapor is a rapid thermal heating apparatus, such as but not limited to, the Radiance Centura, available from Applied Materials, Inc. of Santa Clara, Calif. One embodiment of a rapid thermal heating apparatus is disclosed in U.S. Pat. No. 6,037,273, entitled "Method and Apparatus for lnsitu Vapor Generation," assigned to Applied Materials, Inc. of Santa Clara, Calif., which is a Continuation-In-Part Application to U.S. patent application Ser. No. 08/893,774, both of which are incorporated by reference in their entirety to the extent not inconsistent with the present disclosure.
In step  1901, a pulse of an aluminum precursor is introduced through the lid assembly into the chamber proximate the substrate surface. In step 1902, a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. In step 1904 or in step 1905, a pulse of a hydrogen/oxygen content vapor provided to the substrate surface. The relative amounts of hydrogen and oxygen in the vapor may be adjusted during cycling or may remain at a fixed level. Generally, the vapor concentrations run into oxygen rich vapors comprising mostly oxygen and hydrogen rich vapors comprising mostly hydrogen. Either or both types of vapors may be used during a given cycle. In step 1906, a purge gas is introduced through the lid assembly into the chamber as a pulse or is continuously flowed in which the pulses of the precursors are dosed therein. The deposition cycle can continue back to the aluminum precursor pulse 1901 if it is determined at step 1907 that additional film thickness is desired or can be terminated if the desired film thickness is deposited as indicated at step 1922. An annealing step 1910 and/or an oxidizing treatment 1911 may be performed after every deposition cycle, or after any number of cycles are performed.
It is to be appreciated that the actual cycle times, pulse times of precursors, pulse times of oxidizing agents, purge times, anneal times, oxidizing treatments, and/or evacuation times of the method as described above in reference to FIGS.  11-19 may vary between cycles or remain constant during a pre-determined number of cycles. In addition, one or more of the methods as described in reference to FIGS. 11-19 may be combined.
an injection plate mounted on the lid and having a recess, and a bottom surface of the recess having a plurality of apertures, the apertures limited to an area proximate a central portion of the substrate receiving surface.
2. The substrate processing chamber of claim 1, further comprising one or more inlet passages formed through the lid in fluid communication with the recess of the injection plate.
3. The substrate processing chamber of claim 2, wherein a fluid flow path is defined through the inlet passages of the lid, through the recess of the injection plate, and through the apertures of the recess of the injection plate.
4. The substrate processing chamber of claim 1, wherein the injection plate includes one or more bosses maintaining a spaced-apart relation between the injection plate and the lid.
5. The substrate processing chamber of claim 1, further comprising a fluid injection system coupled to the lid and in fluid communication with the one or more inlet passages.
a gap defined between the top liner and the bottom liner to allow a purge gas to be introduced therethrough.
7. The substrate processing chamber of claim 6, wherein the bottom liner includes a plurality of ledges adapted to support the top liner thereon.
8. The substrate processing system of claim 7, wherein the top liner further comprises one or more fingers for aligning with one or more of the ledges of the bottom liner.
9. The substrate processing chamber of claim 6, wherein a channel is formed along the interior bottom wall of the chamber body in fluid communication with the gap between the top liner and the bottom liner.
10. The substrate processing system of claim 9, further comprising a purge gas inlet formed at the interior bottom wall in fluid communication with the channel.
two or more exhausts selectively coupled to the interior cavity.
12. The substrate processing chamber of claim 11, further comprising a fluid injection system coupled to the lid assembly, the fluid injection system comprising two or more valves.
13. The substrate processing chamber of claim 12, wherein the two or more exhausts are synchronized with the two or more valves.
14. The substrate processing chamber of claim 11, further comprising at least one diverter to couple at least one gas source selectively between the interior cavity and between at least one of the exhausts.
15. The substrate processing chamber of claim 11, wherein the two or more exhausts are synchronized with the at least one diverter.
providing a purge gas to the region adjacent the substrate surface between the pulse of the aluminum precursor and the pulse of the oxidizing agent.
17. The method of claim 16, further comprising performing an in-situ anneal substrate after a selected number of cycles.
18. The method of claim 16, wherein selected pulses of the oxidizing agent are provided for a prolonged time period.
19. The method of claim 16, further comprising forming one or more additional dielectric material layers over the aluminum oxide layer.
20. The method of claim 16, wherein the oxidizing agent is a controllable hydrogen and oxygen content water vapor.


text:
Q: Multiple small kafka clusters or big shared cluster using AWS MSK We are trying to setup Kafka clusters using AWS MSK (Managed streaming for Kafka). We have multiple use cases where we may need >50 topics each having 5-25 partitions and cumulatively ~100 million events being produced in a single day.
Producer count  - ~75
Consumer count - ~150
Taking cost into consideration (infrastructure and monitoring/maintenance)
Is it good to have multiple small clusters or few large shared clusters?
I understand some drawbacks of having large shared clusters where if one cluster goes down, it affects all topics, but maintenance and cost also play a big role where I feel having few large shared clusters might be preferable.

redpajama_set_name: RedPajamaStackExchange


Moonrocks. The cove used to be called Moonrock Cove, I guess? I cannot imagine why!
The teeny wee babies had black and white striped legs and the big ones bright blue.
Resting on a fallen log.
We always stop at this ice cream parlour in Petaluma.
What am amazing little getaway. I need to check out this state park at some point. It looks incredible.
But we had missed these tidepools somehow!
Aaahhh, your photos always make my jaw drop!
Ummm, can we go here when I come? I need to see anemones.
So beautiful! I dreamt I was buying scarves for my trip!
Yes! Orabelle has been broken since the week after we got here because we can't afford to have her fixed, but we will try before you get here!
I love tidepools with all their creatures and colors, and these photos are stunning. I think this weekend away was a very worthwhile idea.
Gorgeous. I am jealous of the ocean views there. Underwater creatures!


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\section{Introduction}
Single image super-resolution (SISR) aims to reconstruct a visually  natural high-resolution  image from its degraded low-resolution (LR) image.  And it has very wide application on  security and surveillance imaging \cite{gunturk2004super,zou2012very}, medical imaging \cite{shi2013cardiac},  as well as satellite and aerial imaging \cite{yildirim2012novel}.  In real-world scenarios, it is very common and  necessary for SISR to zoom in the LR image with  the user-customized scale factor.  As with the common image viewer, the user can arbitrarily zoom in the viewed image by rolling the mouse wheel to see the local details of the viewed image. The customized scale factor for super-resolution  also can be any positive number. And it should not be fixed to some certain integers. Thus, a  method to solve  super-resolution of arbitrary scale factor is important for putting the SISR into more practical use. If we train a specific model for each positive scale factor, it is impossible to store all these models and it is  inefficient in computing. Thus, the more important thing is
that whether we can  solve the super-resolution of arbitrary scale factor with a single  model.

However, as we all known, the most existing SISR methods only consider super-resolution of some certain integer scale factors (X2, X3, X4). And these methods treat super-resolution of different scale factors as independent tasks. Few previous work has discussed how to implement super-resolution of arbitrary scale factor. As for the state-of-the-art  SISR methods, such as  ESPCNN \cite{shi2016real}, EDSR \cite{lim2017enhanced}, RDN \cite{zhang2018residual} and RCAN \cite{zhang2018image},  these methods zoom in the feature maps at the end of networks with the sub-pixel convolution \cite{lim2017enhanced}. Unfortunately, these methods have to design a specific upscale module  for each scale factor. Each upscale module can only zoom in the image with the fixed integer scale factor. And the sup-pixel convolution only works for the integer scale factors.  These disadvantages limit the use of SISR to real-world scenarios. Although, we could implement  super-resolution of non-integer scale factors by properly upscaling the input image.  However, the repeated computation and the upscaled input make these methods very time-consuming and hard to put into pratical use.

To solve these drawbacks and put SISR into more practical use,   an efficient and novel  method for super-resolution of arbitrary scale factor with a single model is necessary.  If we want to  solve the super-resolution of arbitrary scale factor with a single model, a group of weights for upscale filters is necessary for each scale factor. Inspired by the meta-learning, we propose a network to dynamically predict the weights of  filters for each scale factor. Thus, we no longer need to store weights for each scale factor. Compared with storing the weights for each scale factor,  storing the small weight prediction network is more convenient.

We call this  method Meta-SR. There are two modules in our Meta-SR, the Feature Learning Module and the Meta-Upscale Module.  The  Meta-Upscale Module is proposed to replace the typical upscale module.
For each pixel ${(i,j)}$ on the generated HR image,  we  project it onto the LR image based on the scale factor ${r}$.  The projection coordinate is (${\lfloor \frac ir \rfloor,  \lfloor \frac jr \rfloor)}$ on the LR image.  Our Meta-Upscale Module  takes this coordinate-related and scale-related vector as input and predicts the weights for the filters.  For each pixel ${(i,j)}$ on the generated SR image,  a convolution operation is conducted between the feature at the corresponding projection coordinate on the LR image and the weights of the filters to generate the pixel value on ${(i,j)}$.
The proposed  Meta-Upscale Module could dynamically predict the variant number of  weights for the convolution filters by taking a sequence of  scale-related and coordinate-related vectors as input. Through this way , our Meta-Upscale Module can zoom in the feature maps of arbitrary scale factor with a single model.  Actually, our Meta-Upscale Module can be incorporated into most previous methods \cite{zhang2018residual, zhang2018image, lim2017enhanced} by replacing the typical upscale module.

We present extensive experiments on multiple benchmark datasets for single image super-resolution to evaluate our method. We show that: 1) For super-resolution of single integer scale factor,  our Meta-SR could achieve the comparable results with the corresponding baseline which re-trained the model for each integer scale factor. Note that our Meta-SR is trained a single model for super-resolution of arbitrary scale factor together. 2) For super-resolution of arbitrary scale factor with a single model, our Meta-SR  is  better than these methods based on properly zooming in the input images or the output images, or interpolating on the feature maps. 3) Our Meta-Upscale Module only consists of several fully connected layers and it is fast enough. The running time of our Meta-Upscale is about 1\% of the time consumed by the Feature Learning Module (RDN \cite{zhang2018residual}).

\section{Related Work}
\subsection{Single Image Super Resolution}
Early SISR methods are exemplar or dictionary based super-resolution \cite{chang2004super, timofte2013anchored,tai2017memnet}. These methods require a database of external images and generate the high-resolution images by transfering the relevant patches in the database images. The performance is limited by the size of the database or the dictionary. These traditional methods are very time-consuming and they have limited performance.

With the rapid development of the deep learning, numerous deep learning based methods have been proposed. A three-layers convolutional neural network is firstly proposed by Dong et al. \cite{dong2014learning} called SRCNN. The SRCNN upscaled the low-resolution image with bicubic interpolation before feeding into the network.  Kim et al. \cite{kim2016accurate} increased the depth of the network and used the residual learning for stable training.  Kim et al. \cite{kim2016deeply} firstly introduced the recursive learning to SISR, called DRCN. Tai et al. \cite{tai2017image} proposed DRRN by introducing the recursive blocks with shared parameters to make the training stable.
Tai et al. also introduced the memory block called Memnet \cite{tai2017memnet}.
However, the input  of  these  networks  have  the  same  size  as  the  final  high-resolution image, these methods are time-consuming.

Shi et al. \cite{shi2016real} firstly  proposed a real-time super-resolution algorithm ESPCNN by proposing the sub-pixel convolution layer. The ESPCNN \cite{shi2016real} upscaled the image at the end of the network to reduce the computation.
Ledig et al. \cite{ledig2017photo} introduced the residual block and the adversarial learning \cite{goodfellow2014generative,ganin2014unsupervised}
to make the generated images more realistic and natural. Lim et al. \cite{lim2017enhanced} used the deeper and wider residual networks called EDSR. The EDSR \cite{lim2017enhanced} removed the BN layer and used the residual scaling to speedup the training. Lim also firstly  trained single model for multiple scale factors (X2, X3, X4) called MDSR. The MDSR has different image processing blocks and upscale modules for each scale factor. Zhang et al. \cite{zhang2018residual} proposed a residual dense network (RDN) which combines the advantage of the residual block and the dense connected block. Then Zhang et al. \cite{zhang2018image} introduced the residual channel attention to the SR framework. Wang et al. \cite{Wang_2018_CVPR} proposed a novel deep spatial feature transform to recover textures conditioned on the categorical priors. Both DBPN \cite{Haris_2018_CVPR} and DSRN \cite{Han_2018_CVPR} made use of the mutual dependencies of low-  and high-resolution images. DBPN exploited iterative up-sampling and down-sampling layers to provide  an error feedback mechanism for each stage.  Jo et al. \cite{Jo_2018_CVPR} introduced the dynamic upsampling filters for video super-resolution. The dynamic upsampling filters were generated  locally and dynamically depending on the spatial-temporal neighborhood of each pixel in LR frames.  Different from this work, our  Meta-Upscale Module predicted the weights of the convolution kernel depending on the  varying scale factors for SISR. Moreover, our Meta-Upscale could generate variant number and variant weights of the convolution kernel depend on the scale factor. Instead of using the spatial-temporal feature blocks, the input of the our Meta-Upscale Module is the scale-related and coordinate-related vector. Moreover, our Meta-Upscale Module is proposed to solve the arbitrary scale.

 \begin{figure*}[]
\begin{center}
\includegraphics[width=0.95\linewidth]{framework10.png}
\end{center}
   \caption{An instance  of our Meta-SR based on RDN \cite{zhang2018residual}. We also call the network Meta-RDN.  (a) The Residual Dense Block proposed by RDN \cite{zhang2018residual}.  (b) The Feature Learning Module which  generates the shared feature maps  for arbitrary scale factor. (c) For each pixel on the SR image,  we project it onto the LR image.  The proposed Meta-Upscale Module takes a sequence of  coordinate-related and scale-related vectors as input to predict the weights for convolution filters.  By doing the convolution operation, our Meta-Upscale finally generate the HR image.  }
\label{fig:ecssd3}
\end{figure*}

\subsection{Meta-Learning}
The  meta-learning, or learning to learn, is the science of observing how different machine learning  approaches perform on a wide range of learning tasks, and then learning from this experience, or meta-data. The meta-learning is mainly used in few-shot/zero-shot learning \cite{andrychowicz2016learning,ravi2016optimization} and transfer learning \cite{wang2016learning}. The detailed survey of the meta-learning can be found in \cite{lemke2015metalearning}. Here we only discuss the weight prediction related work.

The weight prediction is  one of  meta-learning strategy in the neural network \cite{lemke2015metalearning}. The weights of the neural network are predicted by another neural network rather than directly learned from the training dataset. Cai et al. \cite{Cai_2018_CVPR} predicted the parameters W of the classifier to adapt to the new categories without back propagation for few-shot learning. The parameters were predicted conditioned on the memory of  the support set. In the object detection task, Hu et al. \cite{hu2017learning} proposed to predict the mask weights from box weights. And Yang et al. \cite{yang2018metaanchor}  proposed a novel and flexible anchor mechanism for object detection. The anchor functions could be dynamically generated from the arbitrary customized prior boxes. In the video super resolution, Jo et al. \cite{Jo_2018_CVPR} proposed a dynamic upsampling filters.  The dynamic upsampling filters were generated locally and dynamically depending on the spatial-temporal neighborhood of each pixel in multiple LR frames.  Unlike this work,  we take the advantage of the meta-learning to predict weights of the filters for each scale factor. We no long need to store the weights of the filters for each scale factor. Our Meta-SR can train a single model for super-resolution of arbitrary scale. It is convenient and efficient for practical use.

The most related work is the Parameterized Image Operators \cite{fan2018decouple} which took  advantage of the weight prediction to dynamically adjust the weights of a deep network for image operators (image filtering or image restoration). Different from this work, our Meta-SR focuses on reformulation of the Upscale Module by taking both the coordinate and scale factor as inputs.

\section{Our Approach}
In this section, we describe the proposed model architectures.  As shown in Fig.\ref{fig:ecssd3}. In our Meta-SR, the Feature Learning Module extracts the feature of the low-resolution image  and the Meta-Upscale Module  upscales the feature map with arbitrary scale factor.  We  introduce our Meta-Upscale at first, then we describe the architecture details of our Meta-SR.
\subsection{Meta-Upscale Formulation}
 Given an LR image ${\textbf{I}^{LR}}$ which is downscaled from the corresponding original HR image ${\textbf{I}^{HR}}$,  the task of SISR is to generate  a HR image ${\textbf{I}^{SR}}$ whose ground-truth is ${\textbf{I}^{HR}}$. We choose the RDN \cite{zhang2018residual} as our Feature Learning Module. As shown in Fig.\ref{fig:ecssd3}(b).  Here, we focus on formulating  the Meta-Upscale Module.

 Let  ${\textbf{F}^{LR}}$ denote the feature extracted by the Feature Learning Module. Suppose  the scale factor is ${r}$. For each pixel ${(i,j)}$ on the SR image, we think that it is decided by the feature of the pixel  ${(i',j')}$ on the LR image and the weights of the corresponding filter.  From this perspective,  the upscale module can be seen as  a  mapping function to map  ${\textbf{I}^{SR}}$  and ${\textbf{F}^{LR}}$.    At first, the upscale module should   map the pixel  ${(i,j)}$ to the pixel  ${(i',j')}$.
Then,   the upscale module needs a specific filter to map the feature of the pixel ${(i',j')}$ to generate the value of this pixel ${(i,j)}$. We formulate the upscale module as:
 \begin{equation}
\label{eq:1}
\textbf{I}^{SR}(i,j) =\Phi(\textbf{F}^{LR}(i',j'), \textbf{W}(i,j))
\end{equation}
where ${\textbf{I}^{SR}(i,j)}$ denotes the pixel value at ${(i,j)}$ on SR image. ${\textbf{F}^{LR}(i',j')}$ denotes the feature  of pixel ${(i',j')}$ on the LR image. ${\textbf{W}(i,j)}$ is the weights of filter for pixel ${(i,j)}$. $ \Phi(.)$ is the feature mapping function  to calculate the pixel value.

 Since each pixel on the SR image corresponds to a filter.  For different scale factors,  both the number of the filters and the weights of the filters are different from the other scale factor.  In order to solve the super-resolution of arbitrary scale factor with a single model,  we propose the Meta-Upscale Module  to dynamically  predict the weights ${\textbf{W}(i,j)}$ based on the scale factor and coordinate information.

 For the  Meta-Upscale Module, there are three important functions.  That is, the Location Projection, the Weight Prediction and the  Feature Mapping.  As shown in the Fig.\ref{fig:ecssd2}. The Location Projection  projects  pixel onto  the LR image. And the Weight Prediction Module predicts the weights of the filter for each pixel on the SR image.
At last, the Feature Mapping function maps the feature on the LR image with the predicted weights  back to  the SR image to calculate the value of the pixel.

 \textbf{Location Projection} For each pixel ${(i,j)}$ on the SR image,
the location projection is to find the ${(i',j')}$ on the LR image. We think the value of the pixel ${(i,j)}$ is decided by  the feature of ${(i',j')}$ on the LR image. We do the following projection operator to map these two pixels:
\begin{equation}
\label{eq:1}
(i',j') = T(i,j) = \left(\left\lfloor \frac ir \right\rfloor ,  \left\lfloor \frac jr \right\rfloor\right) \\
\end{equation}
where T is the transformation function. ${\lfloor \rfloor}$ is floor function.

The Location Projection can be seen as a kind of variable fractional stride \cite{long2015fully} mechanism which could upscale the feature maps with arbitrary scale factor. As shown in the Fig \ref{fig:ecssd2}, if the scale factor ${r}$ is 2, each pixel ${(i',j')}$ determines two points. However, if the scale factor is non-integer, such as r = 1.5, some pixels determine two pixels and some pixels determine one pixel. For each pixel ${(i,j)}$  on the SR image, we could find a unique pixel ${(i',j')}$ on the LR image and we think these two pixels are most related.

 \textbf{Weight Prediction} For the typical upscale module, it predefines the number of filters for each scale factor and learns ${\textbf{W}}$ from the training dataset. Different from the typical upscale module, our Meta-Upscale Module uses a network  to  predict the weights of the filters.
We can formulate the weight prediction as:

 \begin{equation}
\label{eq:1}
\textbf{W}(i,j) = \varphi(\textbf{v}_{ij};\theta) \\
\end{equation}
 where ${\textbf{W}(i,j)}$ are the  weights of filter for pixel ${(i,j)}$ on the SR image, ${\textbf{v}_{ij}}$ is a vector related with ${i,j}$.
 ${\varphi(.)}$ is weight prediction network and takes the  ${\textbf{v}_{ij}}$  as input. ${\theta}$ is the parameters of the weight prediction network.

 \begin{figure}
\begin{center}
\includegraphics[width=0.80\linewidth]{project2.png}
\end{center}
   \caption{The schematic diagram for how to upscale the feature map with  the non-integer scale factor ${r=1.5}$. Here we only show the one-dimensional case for simplify.}
\label{fig:ecssd2}
\end{figure}

 As for the input of  ${\varphi(.)}$ for pixel ${(i,j)}$, the proper choice is the relative offset to the  ${(i',j')}$, the ${\textbf{v}_{ij}}$  can be formulated as:
   \begin{equation}
\label{eq:1}
\textbf{v}_{ij}= \left(\frac ir - \left\lfloor \frac ir \right\rfloor, \frac jr - \left\lfloor  \frac jr \right\rfloor\right)\\
\end{equation}

In order to train the multiple scale factor together, it is  better to add the scale factor into the ${\textbf{v}_{ij}}$ to differentiate the weights for different scale factor. For example, if we want to upscale the image with scale factor 2 and 4, and we denote them as $I^{SR}_2$ and  $I^{SR}_4$ respectively. The pixel $(i,j)$ on $I^{SR}_2$  would have the same weights of the filter  and the same projection coordinate with the pixel $(2i,2j)$ on $I^{SR}_4$. That means that  $I^{SR}_2$ is the subimage of the $I^{SR}_4$.
It would limit the performance. Thus, we redefine the ${\textbf{v}_{ij}}$  as:
\begin{equation}
\label{eq:1}
\textbf{v}_{ij}= \left(\frac ir - \left\lfloor \frac ir \right\rfloor, \frac jr - \left\lfloor  \frac jr \right\rfloor,\frac 1r\right)\\
\end{equation}

 \textbf{Feature Mapping}    We extract  the feature of the ${(i',j')}$ on the LR image from ${\textbf{F}^{LR}}$. And  we predict the weights of the filters with weight prediction network. The last thing we need to do is  mapping  feature to the value of the pixel on the SR image.  We choose the matrix product as the Feature Mapping function. We formulate the ${\Phi (.) }$as:

   \begin{equation}
\label{eq:1}
\Phi(\textbf{F}^{LR}(i',j'),\textbf{W}(i,j))=  \textbf{F}^{LR}(i',j')  \textbf{W}(i,j)\
\end{equation}

Our Meta-Upscale Module is shown in Algorithm \ref{alg::get}.

\begin{algorithm}[h]
\caption{Meta Upscale Module}
\label{alg::get}
\begin{algorithmic}[1]
\Require
scale:${r}$, the size of input image: ${(inH,inW)}$, the weight prediction function:W,  the feature: ${\textbf{F}^{LR}}$
\Ensure
  the upscale image

  \State  Calculate the output size ${outH}$ = int(${inH \times r}$), ${outW}$ = int(${inW \times r}$)
  \For{i = 0 : 1 :  ${outH}$}
      \For{j = 0 : 1 : ${outW}$}
           \State ${v_{ij}= (\frac ir - \lfloor \frac ir \rfloor, \frac jr - \lfloor  \frac jr \rfloor, \frac 1r)}$
           \State ${(i',j')=( \lfloor \frac ir \rfloor, \lfloor \frac jr \rfloor)}$
           \State  the feature on ${(i',j')}$: ${\textbf{F}^{LR}(i',j')}$
           \State  weight predicted by ${\varphi }$: ${\textbf{W}(i, j)}$
           \State ${\textbf{pv} = \textbf{F}^{LR}(i',j') \cdot \textbf{W}(i,j)}$
           \State   the  pixel value on ${(i,j)}$ is ${\textbf{pv}}$
      \EndFor
  \EndFor

  \end{algorithmic}
\end{algorithm}

\subsection{Architecture Details of Meta-SR}
There are two modules in our Meta-SR network, the Feature Learning Module, and the Meta-Upscale Module.
Most the state-of-the-art methods \cite{shi2016real,zhang2018residual,lim2017enhanced,ledig2017photo, Zhang_2018_CVPR} could be selected  as our Feature Learning Module. The proposed Meta-Upscale Module could be applied to these networks by simply replacing the traditional upscale module (sub-pixel convolution \cite{shi2016real}).
We choose the state-of-the-art SISR network, called  residual dense network ( RDN \cite{zhang2018residual} )  as   our Feature Learning Module.  Note that our Meta-SR can also work with EDSR or MDSR \cite{lim2017enhanced} or RCAN \cite{zhang2018image}.  For the RDN \cite{zhang2018residual}, there are  3 convolutional layers and 16 residual dense blocks (RDBs). Each RDB has 8 convolutional layers. The growth rate for the dense block is 64.  And the extracted feature map has   64 channels. The detailed structure  is shown in Fig.\ref{fig:ecssd3}.  More details can be found in RDN \cite{zhang2018residual}.

 For the Meta-Upscale Module,  it consists of several fully connected layers and several activation layers. Each input will output one group of  weights with the shape ${(inC, outC, k, k)}$.  Here the ${inC}$ is the number of channels of the extracted feature map, and the ${inC =64}$ in the paper.  The ${outC}$ is the number of channels of the predicted HR image. Generally, ${outC=3}$ for color images and ${outC=1}$ for grayscale image.  The ${k}$ represents the size of the convolution kernel.

 Here we want to describe the parameters of the proposed Meta-Upscale Module including the number of hidden neurons, the number of the fully connected layers, the choice of  activation function and the kernel size of the convolution layer.  Since the output size ${(k^2\times inC \times outC)}$ is very large compared with the input size (3), we set the  number of the hidden neurons as 256.  Continuing to increase the number of the hidden neurons has no improvements. And  the activation function is  ReLU. We conduct experiments and find that the best number of the fully connected layer is 2 with the balance of the speed and the performance.
As for the kernel size, ${3 \times 3}$ is the best size . Conducting ${5 \times 5}$ convolution operation on the large feature maps is more time-consuming.

\begin{table*}[h]
\caption{Results of arbitrary upscale on different methods.  The EDSR is  based on residual block. And the RDN is based on the dense connection block. The test dataset is B100 \cite{martin2001database}. The Best  results is ${\textbf{black}}$.}
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline

\diagbox{Methods}{Scale} &X1.1 & X1.2 &X1.3 & X1.4 &X1.5 &X1.6 &X1.7 &X1.8&X1.9&X2.0 \\
\hline
bicubic & 36.56 & 35.01 & 33.84 & 32.93 & 32.14&31.49&30.90&30.38&29.97& 29.55 \\
\hline

RDN(x1) &  42.41 &  39.76 &  38.00 &  36.68 &  35.57 &   34.64 &  33.87 &   33.19 & 32.60 & 32.08    \\

RDN(x2) & 41.84 & 39.34 & 37.87 & 36.63 & 35.56  &34.63 &33.83 &33.1 &32.52 &  32.11  \\

RDN(x4) & 39.71 & 38.48 & 37.33 & 36.29 & 35.34 &34.52&33.81 &33.14&   32.60& 32.09  \\
BiConv & 41.86 & 39.16 & 37.88 & 29.86 & 35.68  &34.77 &33.95 &33.18 &32.60 &  31.85  \\
Meta-Bi & 42.11 & 39.58 & 38.07 & 36.83 & 35.81  &34.86 &34.03 &33.24 &32.63 &  32.18  \\
Meta-RDN(\textbf{our}) & \bfseries 42.82 & \bfseries 40.40 &\bfseries 38.28 & \bfseries 36.95 &\bfseries 35.86 & \bfseries 34.90 & \bfseries 34.13 & \bfseries 33.45 & \bfseries 32.86 & \bfseries 32.35 \\
\hline
EDSR(x1) &  42.42 &  39.79 &  38.08 &  36.73 &  35.65 &  34.73  &  33.83 &  33.27 &  32.67 &   32.15  \\

EDSR(x2) & 41.79 &39.11& 37.79 & 36.51 & 35.40 & 34.49 &33.81  &33.11 &32.57 & 32.09  \\

EDSR(x4) & 39.61 & 38.41 & 37.27 & 36.24 & 35.30 &34.46  &33.75 &33.09 & 32.56  & 32.04  \\
Meta-EDSR(\textbf{our}) & \bfseries 42.72 & \bfseries 39.92 & \bfseries 38.16 & \bfseries 36.84 &  \bfseries35.78 &  \bfseries 34.83 & \bfseries 34.06 & \bfseries 33.36 & \bfseries 32.78& \bfseries 32.26\\
\hline
\hline

\diagbox{Methods}{Scale} &X2.1 & X2.2 &X2.3 & X2.4 &X2.5 &X2.6 &X2.7 &X2.8&X2.9&X3.0 \\
\hline
bicubic & 29.18 & 28.87 & 28.57& 28.31& 28.13 & 27.89 & 27.66 & 27.51 & 27.31 & 27.19 \\
\hline

RDN(x1) &  31.63 & 31.23 & 30.86 & 30.51 & 30.23 &29.95 &29.68 &29.45 &29.21& 29.03  \\
RDN(x2) & 31.61 &  31.24 & 30.82 & 30.44 & 30.23 &29.71&29.65&29.43&29.20& 29.05  \\
RDN(x4) & 31.61 & 31.23 &  30.88 &   30.52 &   30.31 &  29.99 & 29.75 &  29.53 &  29.26 &  29.14  \\
BiConv & 31.53 & 31.11 & 37.87 & 30.38 & 30.16  &29.81 &29.55 &29.28 &29.05 &  28.91  \\
Meta-Bi & 31.59 & 31.21 & 30.91 & 30.54 & 30.34  &30.01 &29.76 &29.54 &29.28 &  29.22  \\
Meta-RDN(\textbf{our}) &\bfseries 31.82 & \bfseries31.41 & \bfseries 31.06 &\bfseries  30.62 & \bfseries 30.45 &\bfseries  30.13 & \bfseries 29.82 &\bfseries  29.67 & \bfseries 29.40 & \bfseries 29.30\\
\hline
EDSR(x1) &  31.69 &  31.29 & \bfseries30.91 &  30.56 &  30.28 &   29.98  &   29.73 &   29.49 &   29.25 & 29.07  \\

EDSR(x2) &  31.57 & 31.15  & 30.81 & 30.47 & 30.22 &29.91  &29.66 &29.45 &29.19 &   29.09  \\

EDSR(x4) & 31.56 & 31.17 & 30.82 & 30.46 & 30.24 & 29.93  & 29.68 & 29.47  & 29.20 & 29.08 \\
Meta-EDSR(\textbf{our})& \bfseries 31.73 &\bfseries  31.31 &  30.87 &\bfseries  30.60 & \bfseries 30.40 & \bfseries 30.09  &\bfseries 29.83 &\bfseries 29.61 &\bfseries 29.34 & \bfseries 29.22\\
\hline
\hline

\diagbox{Methods}{Scale} &X3.1 & X3.2 &X3.3 & X3.4 &X3.5 &X3.6 &X3.7 &X3.8&X3.9&X4.0 \\
\hline
bicubic & 26.98 & 26.89 & 26.59 & 26.60 & 26.42 & 26.35 & 26.15 & 26.07 & 26.01 & 25.96 \\
\hline

RDN(x1) & 28.81 & 28.67 & 28.47 & 28.30 & 28.15 &28.00  &27.86 &27.72 &27.59 & 27.47\\
RDN(x2) & 28.71 & 28.69 & 28.51 &  28.49 & 28.18& 28.17 &\bfseries28.09&   27.84 &27.61 & 27.51  \\
RDN(x4) & \bfseries 28.89 &  28.75 &   28.57 & 28.42 &  28.19  &28.16 &27.93 &27.81  &   27.70&  27.64  \\
BiConv & 28.64 & 28.51 & 28.28 & 28.13 & 27.91  &27.84 &27.61 &27.49 &27.37 &  27.29  \\
Meta-Bi & 28.89 & 28.75 & 28.54 & 28.39 & 28.17  &28.11 &27.87 &27.75 &27.64 &  27.58  \\
Meta-RDN(\textbf{our}) &  28.87&\bfseries 28.79 &\bfseries 28.68 & \bfseries 28.54 & \bfseries 28.32 &\bfseries 28.27 &  28.04 &\bfseries 27.92 & \bfseries27.82 & \bfseries 27.75  \\
\hline
EDSR(x1) &   28.85 & 28.69 &  28.51 &   28.36 &   28.18 &28.04  &  27.91 &  27.77&   27.64 & 27.52  \\

EDSR(x2) & 28.78 & 28.64 & 28.45 & 28.34 & 28.11 &28.06  &27.83 &27.73 &27.61 & 27.49  \\

EDSR(x4) & 28.82 &   28.69 & 28.49 & 28.35 & 28.13 &   28.09  & 27.85 & 27.73 &27.63 &  27.56  \\
Meta-EDSR(\textbf{our}) &\bfseries 28.95 &\bfseries 28.82 &\bfseries 28.63 &\bfseries 28.48 &\bfseries 28.27 & \bfseries28.21  &\bfseries 27.98 & \bfseries 27.86 & \bfseries 27.75 & \bfseries 27.67\\
\hline
\end{tabular}
\end{center}
\label{table:1}
\end{table*}

\section{Experiments}
\subsection{Datasets and Metrics}
In the NTIRE 2017 Challenge on Single Image Super Resolution,   a high-quality dataset DIV2K \cite{timofte2017ntire} is newly released. There are 1000  images in DIV2K database, 800 images for training, 100 images for validation  and 100 images for test.  All of our models are trained with DIV2K training images set. For testing, we use four standard benchmark datasets: Set14 \cite{zeyde2010single}, B100 \cite{martin2001database}, Manga109 \cite{huang2015single} and DIV2K \cite{timofte2017ntire} . Note that the ground truth of the DIV2K test set is not publicly available. Therefore, we report the results on the DIV2K validation set. The super-resolution results are evaluated with PSNR and SSIM \cite{wang2004image}. Following the setting in \cite{zhang2018residual}, we only consider the PSNR and SSIM \cite{wang2004image} on the Y channel of the transformed YCbCr color space.

As for the degradation methods to generate the low-resolution images, following \cite{lim2017enhanced, zhang2018residual}, we use the bicubic interpolation by adopting the Matlab function imresize to simulate the LR images.

\subsection{Training Details}
In the single image super-resolution, the traditional loss function is L2 loss. Following the setting of \cite{lim2017enhanced}, we train our network using L1 loss instead of the L2 for better convergence.

During training the network,  we randomly extract 16 LR RGB patches with the size of 50*50 as a batch input. Following the setting in \cite{zhang2018residual}, we randomly augment the patches by flipping horizontally or vertically and rotating ${90^\circ}$. The optimizer is Adam. The learning rate is initialized to ${10^{-4}}$ for all the layers and decreases by half for every 200 epochs. All experiments  run in parallel on 4 GPUs. The training scale factors of the Meta-SR vary from 1 to 4 with stride 0.1, and the distribution of the scale factors is uniform. Each patch image in a batch has the same scale factor. Our Meta-SR is trained with Meta-Upscale Module from scratch.

\subsection{Single Model For Arbitrary Scale Factor}

Since no previous approach has focused on the  super-resolution of arbitrary scale factor with a single model,  we need to   design several baselines. We compare our approach with these baselines to prove the superiority of Meta-SR.

Suppose we want to  zoom in  the LR image with scale  ${r \in (1,4]}$. Before we feed it into the network, we could upscale it with bicubic interpolation. Thus, the first baseline simply upscales the LR image with bicubic interpolation as the final HR image, called bicubic baseline.    The second approach upscales the LR image  r times at first, and then input it into a CNN to generate the final HR image, called EDSR(x1) and RDN(x1)  respectively. These two  methods are very time-consuming and hard to put into practical use.

The third baseline  downscales the generated HR image. Suppose there is a network G to implement the ${k}$ times upscale. Thus we could input the LR image into the network G to generate the HR image. And then we downscale the HR image with scale factor ${\frac rk}$ to predict the final results.  If the ${k=2}$, we call them RDN(x2),  and EDSR(x2) respectively. For the scale ${r > k}$, we have to upscale the LR image before feeding it into the network. If the ${k=4}$, it is the fourth baseline. We call them RDN(x4) and EDSR(x4) respectively.

In order to prove the superiority of the Weight Prediction and the Location Projection, we design the fifth baseline (\textbf{BiConv}): we use the interpolation to upscale the final feature maps, the upscale module is fixed convolution layer for all scale factor. And the sixth baseline (\textbf{Meta-Bi}) is interpolating the feature maps to the needed size. We use the  Weight Prediction network to predict the weights of the convolution filter for each scale factor. We train all these models on arbitrary scale factor together.

The experimental results are shown in Table \ref{table:1}.  For the bicubic interpolation baseline, simply upscaling the LR image with bicubic interpolation could not introduce any texture or details to the HR images. It has very limited performance.  For the RDN(x1) and EDSR(x1), it has low-performance on the large scale factors. And the upscaled input makes it time-consuming.
For the RDN(x4) and EDSR(x4), the performance has huge gap between our Meta-RDN and RDN(x4) (or Meta-EDSR and EDSR(x4)) for scale factor close to 1. Moreover,  EDSR(x4) and RDN(x4) also have to upscale the LR image before feeding it into the network when the the scale ${r>k}$.

Thanks to the Weight Prediction, both Meta-Bi and our Meta-SR could learn the best weights of the filter for each scale factor while BiConv shares the same weights of the filter for all the scale factors. The experimental results show that Meta-Bi is significantly better than BiConv which proves the superiority of the Weight Prediction Module.   At the same time, our Meta-RDN is also better than the Meta-Bi. For the interpolation on the feature  maps, the larger the scale factor is, the smaller the valid Filed Of View (FOV) is. However, each scale factor has the same FOV in our Meta-SR methods.
Benefited from the proposed Meta-Upscale, our Meta-RDN  achieves the better  performance on almost all scale factors than the other baselines.

\subsection{The Inference Time}
SISR is low-level image processing task and has very high practical use. In real-world scenarios, the time requirements are very important and strict for SISR.
We measure the computing efficiency using Tesla P40 with Intel Xeon E5-2670v3@2.30GHz. We choose the B100 \cite{martin2001database} as the test dataset. Here, we do not take  the image pre-processing time into consideration.

We conduct experiments to calculate the running time of each module in our Meta-SR and the baselines. As shown in the Table.\ref{table:module}.  Compared with the Feature Learning Module, the running time of our Weight Prodiction Module can be neglected. Because there are only two fully connected layers in our Meta-Upscale Module.

Although the computing efficiency  of  our Meta-SR on single scale  has no  advantage when we compare with the baselines RDN(x1), RDN(x2) and RDN(x4) on scale ${r=2}$. If we increase the scale factor to 8 or 16, our Meta-SR is less time-consuming than these baselines.  Moreover, if we want to continuously zoom in the same image with different scale factors like the common image viewer,  our Meta-SR is the fastest. Since our Meta-SR method only need to run the Meta-Upscale Module for each scale factor. RDN(x1) and RDN(x2)  have to upscale the input image at first. And then they feed the upscaled image into whole network for each scale factor.
Thus,  we claim that our  Meta-RDN is more efficient and has better performance than these baselines.

\begin{table}[t]
\caption{Comparison running time with the baselines. FL represents the Feature Learning Module. WP is Weight Prediction Module of  our Meta-SR. Upscale is the Upscale Module. We test on the B100 and the test scale factor is 2. }
\begin{center}

\begin{tabular}{|c|c|c|c|}
\hline
Methods & FL & WP & Upscale   \\
\hline\hline
RDN(x1) & 3.66e-2s &  - & 1.7e-4s \\
RDN(x2) & 3.29e-2s &  - & 1.9e-4s \\
RDN(x4) & 3.13e-2s &  - & 3.2e-4s \\
Meta-RDN & 3.28e-2s & 1.5e-4s & 3.6e-4s \\
\hline
\end{tabular}
\end{center}
\label{table:module}
\end{table}

\subsection{Comparison With The SOTA Methods}

We apply the proposed Meta-Upscale Module to the  RDN \cite{zhang2018residual}  by replacing the typical upscale module, called Meta-RDN . We train our Meta-RDN on the DIV2K training images with random scale factor ${r \in (1,4]}$. We compare the Meta-RDN with the corresponding baseline RDN \cite{zhang2018residual}. For fair comparison, we also try to finetune our Meta-RDN for each single scale factor. However, fine-tuning on each single integer scale factor have few improvement to the final performance. And  the RDN   re-trained the model for each scale factor with different upscale module, including X2, X3, X4.
We test our  Meta-RDN on four different benchmarks with PSNR and SSIM metrics.

As shown in Table \ref{table:6},  the Meta-RDN achieve the comparable or even better results compared with the corresponding baseline RDN \cite{zhang2018residual}. Since the proposed Meta-Upscale could dynamically predict  weights of the filter for each scale and thanks to the weight prediction, we could train a single model for multiple scale factors and work well at the arbitrary scale factor.
Moreover, our Meta-SR network only need to save one model for test, but the typical model needs to save several models. Our Meta-SR network is more efficient for  SR of multiple scale factors

\begin{table*}[]
\scriptsize
\caption{Compared with the state-of-the-art methods on X2,X3,X4. The reported results of  the state-of-the art  methods are re-trained for each scale factor. }
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\multirow{2}{*}{{Methods}} &
\multirow{2}{*}{Metric} &
\multicolumn{3}{c|}{Set14}&
\multicolumn{3}{c|}{B100}&
\multicolumn{3}{c|}{Manga109} &
\multicolumn{3}{c|}{DIV2K}\\
\cline{3-14}
 & &X2 &X3 &X4 &X2 &X3 &X4 &X2 &X3 &X4 &X2 &X3 &X4  \\
\hline
\multirow{2}{*}{bicubic} & PSNR  &30.24 &27.55 &26.00 &29.56 &27.21 &25.96 &30.80 &26.95 &224.89  &31.35 &28.49 &26.92  \\
& SSIM  &0.8688 &0.7742 &0.7227 &0.8431 &0.7385 &0.6675 &0.9339 &0.8556 &0.7866  &0.9076 &0.8339 &0.7774 \\
\hline
\hline

\multirow{2}{*}{RDN} & PSNR  &34.01 &\bfseries30.57 &28.81 &32.34 &29.26 &27.72 &\bfseries39.18 &34.13 &31.00   &35.17 &31.39 &29.34 \\
& SSIM  &0.9212 &\bfseries0.8468 &0.7871 &0.9017 &0.8093 &0.7419 &0.9780 &\bfseries0.9484 &0.9151   &0.9483 &0.8931 &0.8446 \\
\hline
\multirow{2}{*}{Meta-RDN} & PSNR  &\bfseries34.04 &30.55 &\bfseries28.84 &\bfseries32.35 &\bfseries29.30 &\bfseries27.75 &39.18 &\bfseries34.14 &\bfseries31.03  &\bfseries35.18 &\bfseries31.42 &\bfseries29.36 \\
& SSIM  &\bfseries0.9213 &0.8466 &\bfseries0.7872 &\bfseries0.9019 &\bfseries0.8096 &\bfseries0.7423 &\bfseries0.9782 &0.9483 &\bfseries0.9154  &\bfseries0.9484 &\bfseries0.8935 &\bfseries0.8448 \\
\hline
\end{tabular}
\end{center}
\label{table:6}
\end{table*}

 \begin{figure*}[t]
\begin{center}
\includegraphics[width=0.88\linewidth]{zoom_in.pdf}
\end{center}
   \caption{The visual comparison of an single image upsampling with different scale factors by our Meta-RDN.}
\label{fig:7}
\end{figure*}

\subsection{Visual Results}
In this section, we show the visual results in Fig.\ref{fig:7} and Fig.\ref{fig:8} .
As shown in Fig.\ref{fig:8}, we compare with the RDN(x1), RDN(x2) and RDN(x4) for super-resolution of arbitrary scale factor.  Our Meta-SR has better performance for the structure part. Since the RDN(x1), RDN(x2) and RDN(x4) share the same the weights of filters for all the scale factors, the texture of the SR image generated by these baseline methods is worse than our Meta-RDN. Thanks to the weight prediction,  our Meta-SR can predict a group of independent weights for each scale factor.

 \begin{figure}[t]
\begin{center}
\includegraphics[width=0.95\linewidth]{set14_02_new.pdf}
\includegraphics[width=0.95\linewidth]{b100_42.pdf}
\end{center}
   \caption{The visual comparison with  four baselines. Our Meta-RDN has better performance.}
\label{fig:8}
\end{figure}

\section{Conclusion}
We propose a novel  upscale module named Meta-Upscale to solve the super-resolution of  arbitrary scale factor with a single model. The proposed Meta-Upscale Module  could dynamically predict the weights of the filters. For each scale factor, the proposed Meta-Upscale Module  generates a group of weights for the upscale module.  By doing convolution operation between the feature maps and the filters, we  generate the HR image of arbitrary size. Thanks to the weight prediction, we can train a single model for super-resolution of  arbitrary scale factor. Especially, our Meta-SR can continuously zoom in the same image with multiple scale factors.

\section*{Acknowledgement}
This research is  supported by National Key R\&D Program of China (2017YFA0700800, 2016YFB1001002, 2016YFB1001000), National Natural Science Foundation of China (61525306,
61633021, 61721004, 61420106015), Capital Science and Technology
Leading Talent Training Project (Z181100006318030), and
Beijing Science and Technology Project (Z181100008918010).

\clearpage

{\small
\bibliographystyle{ieee}

redpajama_set_name: RedPajamaArXiv


text:
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The TDC Beatrice Warde Scholarship is sponsored by the Type Directors Club and Monotype in the amount of $5,000. It will be awarded to a female student currently enrolled in her junior undergraduate year and will be applied directly to her senior year tuition, which begins September 2016 and concludes in May 2017.
In addition to the scholarship award, the student will receive an one-year student membership in the TDC.
The scholarship, based solely on merit, will be awarded to a student whose work demonstrates exceptional talent, sophistication, and skill in the use of typography. The criteria for the scholarship extends across disciplines from design criticism to type design and graphic design, since Beatrice Warde was a writer and educator who helped promote Monotype products. Just as Beatrice encouraged the best use of technology, the candidate's work should demonstrate the application of typography to current media, not only print.
The scholarship requirements include a statement and three samples of work accomplished while at school/university, and a grade point average of B or higher.
To apply, submit this form and other application materials by Thursday, 11 February 2016 to director@tdc.org.


Yep, but no break for the Asian Cup.
Fair enough really. To have no HAL for up to 4 weeks over the peak school holiday period because 3 or 4 players are at the Asian Cup would be stupid.
Yeah I agree. Obviously they did it in 2014, but that was because it was hosted here. More so making the point that if he were to make it in the squad then he might be out for a few weeks in Jan.
Didn't realise it's his 150th game.
So it was on mentioned on the Fox podcast that his middle name is Bert.
I'd noticed this on wiki, but tended to assume that was a bit of a jape. So is Bert correct?
Makes you bloody proud. Such a good guy who absolutely deserves it.
Totally made up for the lad.
To see him in the Australian team is just amazing. Watching him in season 1 and especially season 2 of the youth league you could see there was a player.
To go through 2 knee injuries and still make it is awesome.
He deserves it after all the hard work and set backs he's gone through. A great story for Sydney FC too.
Congratulations to @Socceroos cap No.600, @RhyanGrant.
Nice shot of our Rhyan after the game.
Jeez, he only looks about 6.
What are people's favourite memories of Grant? The GF goal is the obvious one.
yeah I could watch that GF goal over and over, and I do sometimes.
Rhyan Grant has admitted approval was legitimately needed for his mullet from the AFC as they don't like offensive hairstyles. Gold.


Forklifts are a wonder at making manual handling tasks easy and efficient. However, while they may minimize the strain to the body from lifting, carrying, pushing, and pulling, they do little to combat injuries caused by static sitting and back twisting. It's typical to see an operator slouching in their seat, leaning forward, twisting to look over their shoulder and/or leaning on the armrest(s). Combine these awkward postures with prolonged use (many operators spend their entire shift seated on the forklift) and whole-body vibration, and the risk of developing and MSD is present.
Provide staff with fully adjustable forklift seating by investigating the options before buying; for example, some forklift seats swivel to reduce twisting demands.
Forklifts may make the job of load handling easier, but that does not mean they are hazard-free. By ensuring we take steps to get the best equipment possible, train on how to best utilize it to minimize injury risk and ensure the facility and work method recommendations are designed to reduce injury risk is the key to addressing this common hazard.
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