Block-sparse Recovery of Semidefinite Systems and Generalized Null Space Conditions

Frederic Matter; Janin Heuer; Marc E. Pfetsch; Thorsten Theobald

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Block-sparse Recovery of Semidefinite Systems and Generalized Null Space Conditions

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arxiv 1907.09442 v3 pith:7IE2A7NT submitted 2019-07-22 cs.IT math.ITmath.OC

Janin Heuer , Frederic Matter , Marc E. Pfetsch , Thorsten Theobald This is my paper · ORCID

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keywords matricesblock-diagonalconditionsrecoverysemidefinitenspsnullspace

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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.

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