The exact group-sparse recovery for block diagonal matrices with subexponential entries

TL;DR

This paper demonstrates that block-diagonal matrices with subexponential entries can achieve exact sparse recovery with nearly optimal measurements, extending classical results for unstructured matrices to structured block-diagonal cases.

Contribution

It provides the first exact recovery guarantees for block-diagonal matrices with subexponential entries, bridging structured and unstructured random matrix theory.

Findings

Exact sparse recovery with nearly optimal measurements

Bounds recover classical results for single-block matrices

Framework applies to highly structured block-diagonal matrices

Abstract

We study block-diagonal random matrices with i.i.d. subexponential entries and show that, despite their highly structured form, they already guarantee exact sparse recovery from a nearly optimal number of measurements. When the matrix reduces to a single block, our framework collapses to the classical i.i.d. subexponential ensemble, and our bounds recover the well-known optimal rates previously established for unstructured random matrices.