Adaptive smoothing algorithms for MBIR in CT applications

Many model based image reconstruction (MBIR) methods for x-ray CT are formulated as convex minimization problems. If the objective function is nonsmooth. primal-dual algorithms are applicable with the drawback that there is an increased memory cost due to the dual variables. Some algorithms recently developed for large-scale nonsmooth convex programs use adaptive smoothing techniques and are of the primal type. That is, they achieve convergence without introducing the dual variables, hence without the increased memory. We discuss one such algorithm with an O(1/k) convergence rate, where k is the iteration number. We then present an extension of it to handle strong convex objective functions. This new algorithm has the optimal convergence rate of O(1/k ²) for its problem class. Our preliminary numerical studies demonstrate competitive performance with respect to an alternative method.