A Convex Penalty for Block-Sparse Signals with Unknown Structures
Hiroki Kuroda, Daichi Kitahara, Akira Hirabayashi
Abstract
We propose a novel convex penalty for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adjusted for the signal of interest by minimizing the mixed ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> /ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> norm over all possible block partitions. Then, by exploiting a variational representation of the ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex penalty. For the resulting regularization model, we provide a proximal splitting-based algorithm which is guaranteed to converge to an optimal solution. Numerical experiments show the effectiveness of the proposed penalty.
BibTeX
@inproceedings{icassp2021_aconvexpenaltyfo,
title = {A Convex Penalty for Block-Sparse Signals with Unknown Structures},
author = {Hiroki Kuroda and Daichi Kitahara and Akira Hirabayashi},
booktitle = {ICASSP 2021},
year = {2021}
}