A Majorize-Minimize memory gradient algorithm applied to X-ray tomography
Résumé
Some recent efforts on image restoration have been extended to tomographic reconstruction methods with a-priori information so that situations with higher amounts of noise or lesser amounts of projections could be better dealt with. This paper deals with the reconstruction of a two- or three-dimensional image from a small set of tomographic projections (i.e. a small number of projection angles). We adopt a variational reconstruction approach, with smooth regularization on the image gradient for reconstruction. The Majorize-Minimize Memory Gradient algorithm is our proposed solution for the optimization problem. The performance of the proposed strategy is illustrated through synthetic and real image reconstruction examples. The reconstruction error is investigated for convex and non-convex penalization strategies, as a function of the number of tomographic measurements and the noise level. The non-convex approach turns out to be more efficient in the case of binary images. In contrast, convex penalization seems to give better results for multi-label or natural images.