SPECT imaging reconstruction through natural pixel discretization

In this paper the problem of reconstructing a two-dimensional tomographic medical image is considered. The emission function is defined on a plane circular domain and has to be reconstructed from data collected by SPECT. Through the natural pixel discretization approach the solution is expressed as a linear combination of functions belonging to a suitable basis. We consider here four different bases, all of them giving a highly structured coefficient matrix. By the Fourier transform the linear system thus obtained can be solved efficiently. The computational cost and the performance of the bases are compared. The numerical experimentation shows that when the data are contaminated by Poissonian noise all the bases are substantially equivalent from the point of view of the reconstruction efficiency.