Sparse Approximate Reconstruction Decomposed by Two Optimization Problems

摘要

We propose a novel sparse signal reconstruction method aiming to directly minimize -quasinorm. Based on the smoothed -quasinorm, we show that there exists an unconstrained optimization problem such that both this problem and the basis pursuit problem are subproblems of the minimization problem. Moreover, we can obtain a sparse solution to the minimization by solving these two subproblems. In addition, we establish the relation between solutions to the minimization and the least square solutions of a linear system. Finally, we present some numerical experiments to illustrate our results.