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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 3567095, 11 pages
Research Article

- and -Norm Joint Regularization Based Sparse Signal Reconstruction Scheme

Southwest Jiaotong University, Chengdu, Sichuan 610031, China

Received 10 May 2016; Revised 7 July 2016; Accepted 10 July 2016

Academic Editor: Nazrul Islam

Copyright © 2016 Chanzi Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 - and -norm joint regularization based reconstruction framework to approach the original -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 -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 -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.