k-Sparse Vector Recovery via $$\ell _1-\alpha \ell _2$$ ℓ 1 - α ℓ 2 Local Minimization

Shaohua Xie (), Jia Li () and Kaihao Liang ()
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Shaohua Xie: Guangdong University of Technology
Jia Li: Sun Yat-Sen University
Kaihao Liang: Zhongkai University of Agriculture and Engineering

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 4, 75-102

Abstract: Abstract This paper studies the $$\ell _1-\alpha \ell _2$$ ℓ 1 - α ℓ 2 local minimization model for $$\alpha \in (0,2]$$ α ∈ ( 0 , 2 ] , which is the first time to consider the case of $$\alpha >1$$ α > 1 . We obtain the necessary and sufficient conditions for a fixed sparse signal to be recovered from this model. Based on this condition, we also obtain the necessary and sufficient conditions for any k-sparse signal to be recovered from $$\ell _1-\alpha \ell _2$$ ℓ 1 - α ℓ 2 local minimization model with $$0

Keywords: Compressed sensing; k-Sparse vector; Local recovery; $$\ell _1-\alpha \ell _2$$ ℓ 1 - α ℓ 2 Minimization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02380-y

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