Abstract:Celebrated breakthrough sparsity theorem obtained independently by Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]} and 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 to P-Type $\ell_1$-minimization problem. In this paper, we extend their result to abstract Banach spaces. We notice that the `normalized' condition for Hilbert spaces can be generalized to a larger extent when we consider Banach spaces.
From: K Mahesh Krishna [view email]
[v1]
Mon, 1 Sep 2025 04:08:09 UTC (8 KB)
[v2]
Tue, 25 Aug 2026 04:00:46 UTC (8 KB)
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