Parallel proximal algorithm for interior tomography problems in x-ray CT with tiny a priori knowledge

Recently, it has been shown that interior tomography problems in x-ray CT can be uniquely determined if tiny subregions inside of the region of interest are known. The solution can be obtained by the projection onto convex sets (POCS) combined with the backprojection filtration algorithm. However, it is well-known that the convergence speed of POCS is slow; hence, to overcome the limitation, this paper employs a parallel proximal algorithm (PPXA) to simultaneously consider multiple convex constraints rather than projecting on each of them sequentially as in POCS. Our simulation results show that the solution for the interior tomography problem can be accurately obtained using PPXA with a much smaller number of iterations than POCS.