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Distribution-aware block-sparse recovery via convex optimization

Daei, S ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1109/LSP.2019.2897861
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2019
  4. Abstract:
  5. We study the problem of reconstructing a block-sparse signal from compressively sampled measurements. In certain applications, in addition to the inherent block-sparse structure of the signal, some prior information about the block support, i.e., blocks containing non-zero elements, might be available. Although many block-sparse recovery algorithms have been investigated in the Bayesian framework, it is still unclear how to incorporate the information about the probability of occurrence into regularization-based block-sparse recovery in an optimal sense. In this letter, we bridge between these fields by the aid of a new concept in conic integral geometry. Specifically, we solve a weighted optimization problem when the prior distribution about the block support is available. Moreover, we obtain the unique weights that minimize the expected required number of measurements. Our simulations on both synthetic and real data confirm that these weights considerably decrease the required sample complexity
  6. Keywords:
  7. Bayesian information ; Block sparse recovery ; Conic integral geometry ; Convex optimization ; Bayesian frameworks ; Bayesian information ; Block sparse ; Block-sparse signals ; Integral geometry ; Optimization problems ; Probability of occurrence ; Synthetic and real data ; Recovery
  8. Source: IEEE Signal Processing Letters ; Volume 26, Issue 4 , 2019 , Pages 528-532 ; 10709908 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/8636201