Projected shrinkage algorithm for box-constrained L1-minimization

Box-constrained L1-minimization can perform remarkably better than classical L1-minimization when correction box constraints are available. And also many practical L1-minimization models indeed involve box constraints because they take certain values from some interval. In this paper, we propose an efficient iteration scheme, namely projected shrinkage (ProShrink) algorithm, to solve a class of box-constrained L1-minimization problems. A key contribution in our technique is that a complicated proximal point operator appeared in the deduction can be equivalently simplified into a projected shrinkage operator. Theoretically, we prove that ProShrink enjoys a convergence of both the primal and dual point sequences. On the numerical level, we demonstrate the benefit of adding box constraints via sparse recovery experiments.