NDLI: Stable recovery of compressed sensing signals via optimal dual frame based ℓ q -minimisation for 0

Content Provider	IET Digital Library
Author	Cao, Chunhong Gao, Xieping
Abstract	Compressed sensing with sparse frame representation has received much greater attention than the orthonormal bases for its practical application in signal processing. One can expect exact recovery from undersampled data via an ℓ q -minimisation under some proper conditions imposed on the sensing/measurement matrix and sparse representation matrix. In this study, the authors first introduce a recovery condition named by B-GRIP, which is actually a generalisation of the well-known restricted isometry property that most of the compressed sensing problems depend on. Under this condition, they expand the performance analysis of compressed sensing problem by an ℓ q -minimisation problem for 0 < q ≤ 1 via the optimal dual frame. Finally, they present an iterative algorithm concerning the restoration of compressed sensing signals based on ℓ q -minimisation for 0 < q ≤ 1 as well as the convergence of the algorithm, and prove that the iterative sequence can not only approximate the original signal, but be the exact one.
Starting Page	296
Ending Page	303
Page Count	8
ISSN	17519675
Volume Number	13
e-ISSN	17519683
Issue Number	Issue 3, May (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/13/3
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2018.5008
Journal	IET Signal Processing
Publisher Date	2018-11-09
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	B-GRIP Compressed Sensing Compressed Sensing Signal Restoration Convergence of Numerical Method Interpolation And Function Approximation Iterative Algorithm Iterative Method Iterative Sequence Linear Algebra Matrix Algebra Minimisation Numerical Analysis Optimal Dual Frame Optimisation Technique Restricted Isometry Property Sensing-measurement Matrix Signal Processing And Detection Signal Processing Theory Signal Representation Signal Restoration Sparse Frame Representation Sparse Representation Matrix Stable Compressed Sensing Signal Recovery Undersampled Data ℓq-minimisation Problem
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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