A Two Stage Generalized Block Orthogonal Matching Pursuit (TSGBOMP) Algorithm
Samrat Mukhopadhyay, and Mrityunjoy Chakraborty

TL;DR
This paper introduces a two-stage algorithm for recovering block sparse signals without assuming uniform block sizes, improving accuracy and robustness over existing methods like BOMP.
Contribution
It proposes a novel two-step procedure for non-uniform block sparse recovery and provides detailed convergence analysis including complex and matrix cases.
Findings
Significantly improved recovery performance over BOMP
High probability bounds for successful recovery with Gaussian sensing matrices
Effective localization of non-zero clusters within signals
Abstract
Recovery of an unknown sparse signal from a few of its projections is the key objective of compressed sensing. Often one comes across signals that are not ordinarily sparse but are sparse blockwise. Existing block sparse recovery algorithms like BOMP make the assumption of uniform block size and known block boundaries, which are, however, not very practical in many applications. This paper addresses this problem and proposes a two step procedure, where the first stage is a coarse block location identification stage while the second stage carries out finer localization of a non-zero cluster within the window selected in the first stage. A detailed convergence analysis of the proposed algorithm is carried out by first defining the so-called pseudoblock-interleaved block RIP of the given generalized block sparse signal and then imposing upper bounds on the corresponding RIC. We also extend…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
