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

Author

Listed:
  • Shaohua Xie

    (Guangdong University of Technology)

  • Jia Li

    (Sun Yat-Sen University)

  • Kaihao Liang

    (Zhongkai University of Agriculture and Engineering)

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

Suggested Citation

  • Shaohua Xie & Jia Li & Kaihao Liang, 2024. "k-Sparse Vector Recovery via $$\ell _1-\alpha \ell _2$$ ℓ 1 - α ℓ 2 Local Minimization," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 75-102, April.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:1:d:10.1007_s10957-024-02380-y
    DOI: 10.1007/s10957-024-02380-y
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