Block‐sparse signal recovery based on truncated ℓ1 minimisation in non‐Gaussian noise

• Published in: IET communications Vol. 13; no. 2; pp. 251 - 258
• Main Authors: Feng, Qingrong, Wang, Jianjun, Zhang, Feng
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 18.01.2019
• Subjects: altemating direction method‐of‐multiplier; augmented Lagrangian methods; 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; reconstruction error; signal reconstruction; truncated ℓ1 minimisation; truncated ℓ1 model; ℓp‐norm functions
• ISSN: 1751-8628; 1751-8636
• DOI: 10.1049/iet-com.2018.5180

This study addresses the issue of block‐sparse recovery in compressive sensing in the presence of non‐Gaussian measurement noise. By using the generalised ℓp‐norm noise constraint for 2≤p<∞ to replace the popular ℓ2‐norm, in this study, the authors put forward a truncated ℓ1 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 ℓp‐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.