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Block-Sparse Recovery with Optimal Block Partition
  • Hiroki Kuroda ,
  • Daichi Kitahara
Hiroki Kuroda
Ritsumeikan University, Ritsumeikan University, Ritsumeikan University

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Daichi Kitahara
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This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.
2022Published in IEEE Transactions on Signal Processing volume 70 on pages 1506-1520. 10.1109/TSP.2022.3156283