On the ℓ₁-Norm Invariant Convex k-Sparse Decomposition of Signals

2013/05/26 by Guangwu Xu, Xu, Guangwu, Zhiqiang Xu +1
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.1305.6021

Add some comments for the noise case

openalex publication_date 2013/05/26 · arxiv created 2013/11/11 · arxiv updated 2013/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by an interesting idea of Cai and Zhang, we formulate and prove the convex k-sparse decomposition of vectors which is invariant with respect to ℓ₁ norm. This result fits well in discussing compressed sensing problems under RIP, but we believe it also has independent interest. As an application, a simple derivation of the RIP recovery condition δ_k+θ_k,k < 1 is presented.

Citations

• Sharp RIP bound for sparse signal and low-rank matrix recovery
• Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices

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