Adaptive efficient sparse estimator achieving oracle properties. Issue 4 (1st June 2013)

• Record Type: Journal Article
• Authors: Yousefi Rezaii, Tohid; Tinati, Mohammad Ali; Beheshti, Soosan
• Is Part Of: IET signal processing. Volume 7:Issue 4(2013)
• Page Start: 259
• Page End: 268
• Publication Date: 2013-06-01
• Subjects: adaptive signal processing -- concave programming -- least mean squares methods -- signal reconstruction; adaptive efficient sparse estimator -- oracle properties -- compressed sensing signal processing -- signal processing context -- nonconvex optimisation problem -- Nyquist lower bound sampling rate -- objective function -- sparse signal -- Lasso objective function -- linearised exponentially decaying‐based objective function -- LED‐ based objective function -- sequential adaptive coordinate‐wise solution -- LED‐SAC reconstruction algorithm -- least mean squared error criterion; adaptive signal processing -- concave programming -- least mean squares methods -- signal reconstruction; adaptive efficient sparse estimator -- oracle properties -- compressed sensing signal processing -- signal processing context -- nonconvex optimisation problem -- Nyquist lower bound sampling rate -- objective function -- sparse signal -- Lasso objective function -- linearised exponentially decaying‐based objective function -- LED‐ based objective function -- sequential adaptive coordinate‐wise solution -- LED‐SAC reconstruction algorithm -- least mean squared error criterion; Signal processing -- Periodicals; 621.3822
• DOI: 10.1049/iet-spr.2012.0386
• Languages: English
• ISSNs: 1751-9675

Abstract

Abstract : Compressed Sensing is the new trend in the signal processing context which aims to sample a compressible signal with a rate less than the Nyquist lower bound sampling rate. The main challenge arises due to the non‐convex optimisation problem to be solved in the reconstruction stage. This paper introduces a suitable objective function in order to simultaneously recover the true support of the underlying sparse signal while achieving an acceptable estimation error. Inspired by the well‐known Lasso objective function, we have developed an objective function based on a new penalty denoted by the Linearised Exponentially Decaying (LED) penalty. The comprehensive analysis of the LED based objective function shows that the new approach satisfies the oracle properties, as opposed to the conventional Lasso objective function. Furthermore, we have developed a Sequential Adaptive Coordinate‐wise (SAC) solution for the proposed objective function. The simulation results for the proposed LED‐SAC reconstruction algorithm are given and compared with other state of the art methods. It is shown that LED‐SAC approaches the least mean squared error criterion. Moreover, compared to the other methods, LED‐SAC has much more adaptation rate in terms of tracking the variations in the support of the underlying sparse signal.