A Study of Numerical Algorithms for Regularized Poisson ML Image Reconstruction

In this report we solved a regularized Poisson maximum likelihood (ML) image reconstruction problem, using various numerical methods. Rather than the commonly assumed Gaussian ML formulation, we considered a Poisson ML formulation, which is more accurate in some applications such as low dose computed tomography (CT), and also avoids the problematic log conversion in the Gaussian formulation. The speed of these methods are compared using a 64 by 64 pixel size example. We found that in our case the diagonally preconditioned conjugate gradient (PCG) method has the best performance.