Performance analysis of partial support recovery and signal reconstruction of compressed sensing. Issue 2 (1st April 2014)

• Record Type: Journal Article
• Authors: Xu, Wenbo; Lin, Jiaru; Niu, Kai; He, Zhiqiang; Wang, Yue
• Is Part Of: IET signal processing. Volume 8:Issue 2(2014)
• Page Start: 188
• Page End: 201
• Publication Date: 2014-04-01
• Subjects: maximum likelihood estimation -- mean square error methods -- probability -- signal reconstruction -- compressed sensing; partial support recovery -- signal reconstruction -- compressed sensing -- sparse signals -- optimal maximum‐likelihood algorithm -- asymptotic mean‐square‐error -- ML algorithm -- SNR -- MSE gain; Signal processing -- Periodicals; 621.3822
• DOI: 10.1049/iet-spr.2011.0205
• Languages: English
• ISSNs: 1751-9675

Abstract

Abstract : Recent work in the area of compressed sensing mainly focuses on the perfect recovery of the entire support for sparse signals. However, partial support recovery, where a part of the signal support is correctly recovered, may be adequate in many practical scenarios. In this study, in the high‐dimensional and noisy setting, the authors develop the probability of partial support recovery of the optimal maximum‐likelihood (ML) algorithm. When a large part of the support is available, the asymptotic mean‐square‐error (MSE) of the reconstructed signal is further developed. The simulation results characterise the asymptotic performance of the ML algorithm for partial support recovery, and show that there exists a signal‐to‐noise ratio (SNR) threshold, beyond which the increase of SNR cannot bring any obvious MSE gain.