Tomographic imaging methods are characterized by the possibility of examining internal structures of an examination object without having to perform invasive interventions thereupon. A possible type of tomographic image generation consists of recording a number of projections of the object to be investigated from various angles. A two-dimensional view or a three-dimensional volume image of the examination object can be calculated from these projections.
Computed tomography is an example of such a tomographic imaging method. Various methods for scanning an examination object with a CT system are known. For example, circular scans, sequential circular scans with a feed or spiral scans are used. Other kinds of scans which are not based on circular movements are also possible, for example scans with linear segments. Absorption data of the examination object is recorded from various angles with the aid of at least one X-ray source and at least one detector on the opposite side and this absorption data or these projections collected in this way are merged to form sectional views through the examination object by way of corresponding reconstruction methods.
To reconstruct computed tomographic images from X-ray CT data sets of a computed tomography device (CT device), i.e. from the recorded projections, a so-called Filtered Back Projection (FBP) is used as a standard method today. After data acquisition a so-called “rebinning” step is usually performed, in which the data generated with the fan-shaped beam spreading out from the source is rearranged in such a way that it exists in a form as if the detector were being hit by parallel X-rays falling in the direction of the detector. The data is then transformed into the frequency range. Filtering takes place in the frequency range, and then the filtered data is back-transformed. With the aid of the data rearranged and filtered in this way a back projection then takes place onto the individual voxels inside the volume of interest. However, on account of their approximative working method there are problems with the classic FBP methods with so-called low-frequency hollow-cone artifacts and spiral artifacts. Furthermore, with classic FBP methods the image sharpness is linked to the image noise. The greater the sharpness achieved, the greater the image noise and vice versa.
The FBP method is part of the group of approximative reconstruction methods. In addition, there is the group of exact reconstruction methods, but this is scarcely used at the present time. Finally, a third group of reconstruction methods comprises the iterative methods.
With iterative reconstruction methods at least some of the aforementioned limitations of FBP can be remedied. With such an iterative reconstruction method, initial image data is first reconstructed from the projection measurement data. For example, a folding back projection method can be used for this purpose. The iterative reconstruction method subsequently creates gradually enhanced image data. For example, synthetic projection data can be created from the initial image data using a “projector”, a projection operator which is intended to map the measurement system as well as possible mathematically. The difference from the measured values is then back-projected using the operator adjointed to the projector and in this way a residual image is reconstructed with which the initial image is updated. The updated image data can in turn be used in a subsequent iteration step to create new synthetic projection data with the aid of the projection operator, therefrom to establish the difference from the measurement signals again and to calculate a new residual image with which the image data of the current iteration level can be improved again, etc. Using such a method, image data can be reconstructed which has relatively good image sharpness and nevertheless low image noise. Examples of iterative reconstruction methods are Algebraic Reconstruction Technology (ART), Simultaneous Algebraic Reconstruction Technology (SART), Iterative Filtered Back Projection (IFBP), as well as statistical iterative image reconstruction technologies.