NDLI: Block-sparse signal recovery based on truncated ℓ1 minimisation in non-Gaussian noise

Content Provider	IET Digital Library
Author	Feng, Qingrong Wang, Jianjun Zhang, Feng
Abstract	This study addresses the issue of block-sparse recovery in compressive sensing in the presence of non-Gaussian measurement noise. By using the generalised ℓ p -norm noise constraint for 2 ≤ p < ∞ to replace the popular ℓ 2 -norm, in this study, the authors put forward a truncated ℓ 1 model for recovering block-sparse signal. A theoretical analysis is first presented to guarantee the validity of proposed method. If the measurement matrix satisfies an extended block restricted isometry property, the reconstruction error is bounded in the optimisation. Moreover, in order to solve the induced optimisation problem effectively, they present an alternating direction method of multipliers via embedding Karush–Kuhn–Tucker system of ℓ p -norm functions into the frame structure of augmented Lagrangian methods. When compared with some of the state-of-the-art methods, the proposed method becomes more competitive.
Starting Page	251
Ending Page	258
Page Count	8
ISSN	17518628
Volume Number	13
e-ISSN	17518636
Issue Number	Issue 2, Jan (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-com/13/2
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-com.2018.5180
Journal	IET Communications
Publisher Date	2018-10-23
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Altemating Direction Method-of-multiplier Augmented Lagrangian Method Block-sparse Signal Recovery Compressed Sensing Compressive Sensing Embedding Karush-Kuhn-Tucker System Extended Block Restricted Isometry Property Gaussian Noise Generalised ℓp-norm Noise Constraint Induced Optimisation Problem Matrix Algebra Measurement Matrix Minimisation NonGaussian Measurement Noise NonGaussian Noise Optimisation Technique Reconstruction Error Signal Processing And Detection Signal Processing Theory Signal Reconstruction Statistics Truncated ℓ1 Minimisation Truncated ℓ1 Model ℓp-norm Functions
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Computer Science Applications

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