Approximate Newton’s method for Tomographic Image Reconstruction

In this report we solved a regularized maximum likelihood (ML) image reconstruction problem (with Poisson noise). We considered the gradient descent method, exact Newton’s method, pre-conditioned conjugate gradient (CG) method, and an approximate Newton’s method, with which we can solve a million variable problem. However, the current version of approximate Newton’s method converges slow. We could possibly improve by finding a better approximate to the Hessian matrix, and still easy to compute its inverse.