A majorize-minimize memory gradient algorithm applied to X-ray tomography

Tomography is an image reconstruction task that may be viewed as a linear inverse problem akin to deconvolution. Recent progresses in optimization methods have made it possible to formulate this task so that fewer projections and higher amounts of noise can be dealt with, making use of a-priori information and domain constraints. In this article, we investigate 3MG, a new optimization method that is highly flexible and effective. In particular, we propose and compare convex and non-convex regularization potentials on both synthetic and real images. We further investigate the possibility to deal with continuous angular integration, i.e. where projections rays are no longer straight lines, but cones. This is encountered in a variety of real-life situations, but is difficult or impossible to deal with exactly using traditional reconstruction algorithms. We show that in this situation it may be beneficial to acquire fewer projections than would be required using classical methods.