l 1 - and l2-Norm Joint Regularization Based Sparse Signal Reconstruction Scheme

Abstract EN

Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations.

This is also the application condition of compressive sensing (CS) which can find the sparse solution from the measurements far less than the original signal.

In this paper, we propose l1- and l2-norm joint regularization based reconstruction framework to approach the original l0-norm based sparseness-inducing constrained sparse signal reconstruction problem.

Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem with l0-norm regularization item.

Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error than l1-norm relaxation approaches can be realized by using the proposed scheme in most cases.

Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach.