An Alternative Lagrange-Dual Based Algorithm for Sparse Signal Reconstruction

Abstract

In this correspondence, we propose a new Lagrange-dual reformulation associated with an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization problem for sparse signal reconstruction. There are two main advantages of our proposed approach. First, the number of the variables in the reformulated optimization problem is much smaller than that in the original problem when the dimension of measurement vector is much less than the size of the original signals; Second, the new problem is smooth and convex, and hence it can be solved by many state of the art gradient-type algorithms efficiently. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples.