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

Guozheng Dai; Tiankun Diao; Hanchao Wang

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arXiv · 2506.17965

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

Guozheng Dai·Tiankun Diao·Hanchao Wang

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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.

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Guozheng Dai, Tiankun Diao, Hanchao Wang. 2025-06-22. The exact group-sparse recovery for block diagonal matrices with subexponential entries. https://arxiv.org/abs/2506.17965

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