A fast majorize minimize algorithm for higher degree total variation regularization

The main focus of this paper is to introduce a computationally efficient algorithm for solving image recovery problems, regularized by the recently introduced higher degree total variation (HDTV) penalties. The anisotropic HDTV penalty is the fully separable L
₁
semi-norm of the directional image derivatives; the use of this penalty is seen to considerably improve image quality in biomedical inverse problems. We introduce a novel majorize minimize algorithm to solve the HDTV optimization problem, thus considerably speeding it over the previous implementation. Specifically, comparisons with previous iterative reweighted algorithm show an approximate ten fold speedup. The new algorithm enables us to obtain reconstructions that are free of patchy artifacts exhibited by classical TV schemes, while being comparable to state of the art total variation regularization schemes in run time.