Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction

Bregman methods introduced in [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460–489] to image processing are demonstrated to be an efficient optimization method for solving sparse reconstruction with convex functionals, such as the $\ell^1$ norm and total variation [W. Yin, S. Osher, D. Goldfarb, and J. Darbon, SIAM J. Imaging Sci., 1 (2008), pp. 143–168; T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323–343]. In particular, the efficiency of this method relies on the performance of inner solvers for the resulting subproblems. In this paper, we propose a general algorithm framework for inverse problem regularization with a single forward-backward…