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Noncommutative Donoho-Elad-Gribonval-Nielson-Fuchs Sparsity Theorem
Version 1
: Received: 15 August 2024 / Approved: 15 August 2024 / Online: 15 August 2024 (14:48:47 CEST)
How to cite: KRISHNA, K. M. Noncommutative Donoho-Elad-Gribonval-Nielson-Fuchs Sparsity Theorem. Preprints 2024, 2024081164. https://doi.org/10.20944/preprints202408.1164.v1 KRISHNA, K. M. Noncommutative Donoho-Elad-Gribonval-Nielson-Fuchs Sparsity Theorem. Preprints 2024, 2024081164. https://doi.org/10.20944/preprints202408.1164.v1
Abstract
Breakthrough Sparsity Theorem, derived independently by Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]}, Gribonval and Nielson \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.
Keywords
sparse solution; frame; hilbert C*-module
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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