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  • 1.
    Wang, Jianfeng
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zhou, Zhiyong
    Department of Statistics, Zhejiang University City College, China.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values2019In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2019, article id 57Article in journal (Refereed)
    Abstract [en]

    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 ℓ2/ℓq and the mixed ℓ2/ℓ1 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 q-ratio BCMSV is bounded away from zero with high probability when the number of measurements is reasonably large. Numerical experiments are implemented to illustrate the theoretical results. In addition, we demonstrate that the q-ratio BCMSV-based error bounds are tighter than the block-restricted isotropic constant-based bounds.

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