Error bounds of block sparse signal recovery based on q -ratio block constrained minimal singular values
作者: Jianfeng WangZhiyong ZhouJun Yu
作者单位: 1Department of Mathematics and Mathematical Statistics, Umeå University
2Department of Statistics, Zhejiang University City College
刊名: EURASIP Journal on Advances in Signal Processing, 2019, Vol.2019 (1), pp.1-12
来源数据库: Springer Journal
DOI: 10.1186/s13634-019-0653-1
关键词: Compressive sensingQ -ratio block sparsityQ -ratio block constrained minimal singular valueConvex-concave procedure
英文摘要: Abstract(#br)In this paper, we introduce the q -ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed ℓ 2 / ℓ q and the mixed ℓ 2 / ℓ 1 norms of the reconstruction errors for stable and robust recovery using block basis pursuit (BBP), the block Dantzig selector (BDS), and the group lasso in terms of the q -ratio BCMSV are investigated. We establish a sufficient condition based on the q -ratio block sparsity for the exact recovery from the noise-free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, the...
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