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.