TechRxiv
BlockSparseRecovery_Kuroda-Kitahara.pdf (3.21 MB)

Block-Sparse Recovery with Optimal Block Partition

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posted on 08.05.2021, 07:06 by Hiroki KurodaHiroki Kuroda, Daichi KitaharaDaichi Kitahara
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.

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Email Address of Submitting Author

kuroda@media.ritsumei.ac.jp

ORCID of Submitting Author

0000-0002-8093-3219

Submitting Author's Institution

Ritsumeikan University

Submitting Author's Country

Japan