Comparison of four natural pixel bases for SPECT imaging

In this paper the problem of restoring a two-dimensional tomographic medical image is considered. The emission function f(P) is defined on a plane circular domain Ω, and has to be restored from data collected by a SPECT machine. Through an approach known as natural pixel discretization, 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. The linear system obtained in this way can be solved efficiently by means of the fast Fourier transform. The computational cost and the performance of the bases are compared. When the data are contaminated by Poissonian noise, the numerical experimentation shows that all the bases are almost equivalent from the point of view of the restoration efficiency. Hence the choice of a basis should rely on other considerations, as for instance the computational cost.