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Compressed sensing with partial support information: coherence-based performance guarantees and alternative direction method of multiplier reconstruction algorithm

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Compressed sensing with partial support information: coherence-based performance guarantees and alternative direction method of multiplier reconstruction algorithm

Content Provider	IET Digital Library
Author	Liu, Haixiao Song, Bin Tian, Fang Qin, Hao
Abstract	The recently introduced theory of compressed sensing (CS) enables the recovery of sparse or compressible signals from a small set of non-adaptive measurements, and furthermore, it holds promise for substantially improving the performance by leveraging more signal structures that go beyond simple sparsity. In this study, the authors study the weighted l 1 minimisation problem for CS reconstruction when partial support information is available. Firstly, they focus on the coherence-based performance guarantees and show that if an estimated support can be obtained with its accuracy and relative size satisfying certain coherence-related conditions, the weighted l 1 minimisation is then stable and robust under weaker sufficient conditions than that of the analogous standard l 1 optimisation. Meanwhile, better upper bounds on the reconstruction error could also be achieved. Besides, a novel adaptive alternating direction method of multipliers with iterative support detection is outlined to solve the weighted l 1 minimisation problem. Simulation results show that the authors’ method achieves good convergence, and obtains improved reconstruction performance in comparison with the conventional methods.
Starting Page	749
Ending Page	758
Page Count	10
ISSN	17519675
Volume Number	8
e-ISSN	17519683
Issue Number	Issue 7, Sep (2014)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/8/7
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2013.0394
Journal	IET Signal Processing
Publisher Date	2014-07-02
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Adaptive Alternating Direction Method Analogous Standard L1 Optimisation Coherence-based Performance Guarantees Compressed Sensing Compressible Signal Convergence Convergence of Numerical Method CS Reconstruction Interpolation And Function Approximation Iterative Method Iterative Support Detection Minimisation Multiplier Reconstruction Algorithm Non-adaptive Measurement Numerical Analysis Optimisation Technique Partial Support Information Relative Size Signal Processing And Detection Signal Processing Theory Signal Reconstruction Signal Structure Sparse Signal Weighted L1 Minimisation Problem
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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