Real Time Tomographic Image Reconstruction in PET Using the Pseudoinverse of the System Response Matrix
Positron Emission Tomography (PET) is one of the most recent medical imaging techniques, and it is commonly used in oncology, cardiology and neurology. PET is based on the detection in coincidence of the two 511 keV photons produced in the annihilation of a positron with an electron of the media. Positrons are emitted by radionuclides linked to a molecule of interest (tracer) administered to the patient. The information of the coincidences of the 511 keV photons is used within a reconstruction algorithm to generate an image of the biodistribution of the tracer in the body. The images are usually obtained after the end of the acquisition, but in some cases it would be useful to be able to obtain PET images in real time. Iterative image reconstruction methods usually provide better resolution and less statistical fluctuations than analytical methods, but they are too slow to be used in real time applications. On the other hand, analytical methods are fast but, they produce images with artifacts when the acquired data are incomplete, they are more sensitive to noise, and their resolution is not optimal as they are based on pure mathematical approaches and assumptions. In this work, we propose to combine the best features of both analytical and iterative methods. We incorporate the most relevant physical processes involved in the emission and detection of the radiation into a System Response Matrix (SRM) and then the reconstruction is obtained using the pseudoinverse (PINV) of the SRM. This method present an improvement in image quality comparing with common real time analytical methods while it is fast enough to be used in real time applications.