Bregman operator splitting with variable stepsize for total variation image reconstruction

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form min{φ(Bu)+ 1/2‖Au− f ‖2}, where φ may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstruction. The stepsize rule starts with a Barzilai-Borwein (BB) step, and increases the nominal step until a termination condition is satisfied. The stepsize rule is related This research was partly supported by National Science Foundation grants 1115568 and 1016204, and by Office of Naval Research grant N00014-11-1-0068. Y. Chen · W.W. Hager · M. Yashtini ( ) Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, FL 32611-8105, USA e-mail: [email protected] url: http://www.math.ufl.edu/~myashtini Y. Chen e-mail: [email protected] url: http://www.math.ufl.edu/~yun W.W. Hager e-mail: [email protected] url: http://www.math.ufl.edu/~hager X. Ye School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, USA e-mail: [email protected] url: http://people.math.gatech.edu/~xye33 H. Zhang Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, USA e-mail: [email protected] url: https://www.math.lsu.edu/~hozhang