Block-sparse Recovery of Semidefinite Systems and Generalized Null Space Conditions
Information Theory
2020-06-29 v3 math.IT
Optimization and Control
Abstract
This article considers the recovery of low-rank matrices via a convex nuclear-norm minimization problem and presents two null space properties (NSP) which characterize uniform recovery for the case of block-diagonal matrices and block-diagonal positive semidefinite matrices. These null-space conditions turn out to be special cases of a new general setup, which allows to derive the mentioned NSPs and well-known NSPs from the literature. We discuss the relative strength of these conditions and also present a deterministic class of matrices that satisfies the block-diagonal semidefinite NSP.
Keywords
Cite
@article{arxiv.1907.09442,
title = {Block-sparse Recovery of Semidefinite Systems and Generalized Null Space Conditions},
author = {Janin Heuer and Frederic Matter and Marc E. Pfetsch and Thorsten Theobald},
journal= {arXiv preprint arXiv:1907.09442},
year = {2020}
}
Comments
23 pages; revised version; accepted for publication in Linear Algebra and Its Applications