Fast artifact free reconstruction algorithm for limited data (PET) using constrained optimisation

The stationary ring of detector systems in positron emission tomography (PET), provide insufficient and unevenly spaced samples per measured projection which lead into artifacts in the reconstruction. Ring motions such as the wobbling motion or the dichotomic sampling motion recently introduced, increase the number of samples but result in highly complex mechanical systems and a substantial increase in data collection time. A very fast direct algorithm is employed here, capable of performing linear interpolation which results in reconstructions shown to be free of the artifacts caused by insufficient sampling. A comparison between this direct algorithm and the convolution and ART methods in terms of speed and reconstruction quality is given