A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula

We present a new reconstruction algorithm for single-photon emission comput ed tomography. The algorithm is based on the Novikov explicit inversion for mula for the attenuated Radon transform with non-uniform attenuation. Our r econstruction technique can be viewed as a generalization of both the filte red backprojection algorithm and the Tretiak-Metz algorithm. We test the pe rformance of the present algorithm in a variety of numerical experiments. O ur numerical examples show that the algorithm is capable of accurate image reconstruction even in the case of strongly non-uniform attenuation coeffic ient, similar to that occurring in a human thorax.