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Noncommutative Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem https://arxiv.org/abs/2409.09060 #mathFA #mathIT #mathOA #mathOC #mathST #statTH #csIT

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

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.

arxiv.org
September 18, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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