In this paper, we present a non-convex l(2)/l(q)(0<q<1)-analysis method to recover a general signal that can be expressed as a block-sparse coefficient vector in a coherent tight frame, and a sufficient conditio...
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In this paper, we present a non-convex l(2)/l(q)(0block-sparse coefficient vector in a coherent tight frame, and a sufficient condition is simultaneously established to guarantee the validity of the proposed method. In addition, we also derive an efficient iterative re-weighted least square (IRLS) algorithm to solve the induced non-convex optimization problem. The proposed IRLS algorithm is tested and compared with the l(2)/l(1)-analysis and the l(q)(0
The mixed l(2)/l(p) (0 < p 1) norm minimisation method with partially known support for recovering block-sparse signals is studied. The authors mainly extend this work on block-sparse compressed sensing by incorpor...
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The mixed l(2)/l(p) (0 < p 1) norm minimisation method with partially known support for recovering block-sparse signals is studied. The authors mainly extend this work on block-sparse compressed sensing by incorporating some known part of the block support information as a priori and establish sufficient restricted p-isometry property (p-RIP) conditions for exact and robust recovery. The authors' theoretical results show it is possible to recover the block-sparse signals via l(2)/l(p) minimisation from reduced number of measurements by applying the partially known support. The authors also derive a lower bound on necessary random Gaussian measurements for the p-RIP conditions to hold with high possibility. Finally, a series of numerical experiments are carried out to illustrate that fewer measurements with smaller p are needed to reconstruct the signal.
compressedsensing is a new sampling technique which can exactly reconstruct sparse signal from a few measurements. In this article, we consider the block-sparse compressed sensing with special structure assumption ab...
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compressedsensing is a new sampling technique which can exactly reconstruct sparse signal from a few measurements. In this article, we consider the block-sparse compressed sensing with special structure assumption about the signal. A novel non-convex model is proposed to reconstruct the block-sparse signals. In addition, the conditions of the proposed model for recovering the block-sparse noise or noise-free signals are presented. The experimental results demonstrate that the proposed non-convex method surpasses the convex method (the mixed -norm optimization) and some algorithms without considering the block-sparse structure (the - and -norm optimization).
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