  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.
