Open AccessBlock‐sparse signal recovery via ℓ 2 / ℓ 1 − 2 minimisation method
Author(s) -
Wang Wendong,
Wang Jianjun,
Zhang Zili
Publication year - 2018
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2016.0381
Subject(s) - signal recovery , block (permutation group theory) , minimisation (clinical trials) , computer science , sparse approximation , algorithm , sparse matrix , signal (programming language) , compressed sensing , mathematics , statistics , physics , geometry , quantum mechanics , gaussian , programming language
Motivated by the recently emerged ℓ 1 − 2method for sparse signal recovery, in this study, the authors make an ongoing effect to extend this methodology to the setting of block sparsity, which directly leads to the proposed ℓ 2 / ℓ 1 − 2method for block‐sparse signal recovery. Some theoretical results are induced to guarantee the validity of proposed method. In particular, the obtained recovery condition rigorously includes the one induced by Yin et al ., and the obtained error estimate can be used to model both the (block‐) sparse and non‐sparse signals, which is more comprehensive than that induced by Yin et al . which applies only to the sparse signals. The authors also derive an alternating direction method of multipliers (ADMM)‐based algorithm to tackle the induced optimisation problem. Some experimental results that are based on the synthetic block‐sparse signals and the real‐world foetal electrocardiogram signals further demonstrate the better performance of the ℓ 2 / ℓ 1 − 2method when it is compared with the state‐of‐the‐art group‐lasso method and ℓ 2 / ℓ q method for 0 < q < 1.