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arXiv · 2409.09060

Noncommutative Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem

K. Mahesh Krishna
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Abstract

Breakthrough Sparsity Theorem, derived independently by Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]}, Gribonval and Nielsen \textit{[IEEE Trans. Inform. Theory, 2003]} and Fuchs \textit{[IEEE Trans. Inform. Theory, 2004]} says that unique sparse solution to NP-Hard $\ell_0$-minimization problem can be obtained using unique solution of P-Type $\ell_1$-minimization problem. In this paper, we derive noncommutative version of their result using frames for Hilbert C*-modules.

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BibTeXRIS

K. Mahesh Krishna. 2024-09-02. Noncommutative Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem. https://doi.org/10.7153/mia-2025-28-33

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