RIP analysis for the weighted ℓr-ℓ1 minimization method
•The restricted isometry property (RIP) and high-order RIP analysis results for the weighted ℓr−ℓ1 minimization method are presented.•Through a novel decomposition of the objective function into a difference of two convex functions, the weighted ℓr−ℓ1 minimization problem is solved via the differenc...
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| Published in: | Signal processing Vol. 202 |
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01.01.2023
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| ISSN: | 0165-1684 |
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| Abstract | •The restricted isometry property (RIP) and high-order RIP analysis results for the weighted ℓr−ℓ1 minimization method are presented.•Through a novel decomposition of the objective function into a difference of two convex functions, the weighted ℓr−ℓ1 minimization problem is solved via the difference of convex functions algorithms (DCA) directly.•Numerical experiments show that the DCA based weighted ℓr−ℓ1 minimization method gives satisfactory results in sparse recovery no matter whether the measurement matrix is coherent or not.•For highly coherent measurements, the proposed method even outperforms the state-of-art ℓ1−ℓ2 minimization method.
The weighted ℓr−ℓ1 minimization method with 0<r≤1 largely generalizes the classical ℓr minimization method and achieves very good performance in compressive sensing. However, its restricted isometry property (RIP) and high-order RIP analysis results remain unknown. In this paper, we fill in this gap by adopting newly developed analysis tools. Moreover, through a novel decomposition of the objective function into a difference of two convex functions, we propose to solve the weighted ℓr−ℓ1 minimization problem via the difference of convex functions algorithms (DCA) directly. Numerical experiments show that our DCA based weighted ℓr−ℓ1 minimization method gives satisfactory results in sparse recovery no matter whether the measurement matrix is coherent or not. For highly coherent measurements, our proposed method even outperforms the state-of-art ℓ1−ℓ2 minimization method. |
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| AbstractList | •The restricted isometry property (RIP) and high-order RIP analysis results for the weighted ℓr−ℓ1 minimization method are presented.•Through a novel decomposition of the objective function into a difference of two convex functions, the weighted ℓr−ℓ1 minimization problem is solved via the difference of convex functions algorithms (DCA) directly.•Numerical experiments show that the DCA based weighted ℓr−ℓ1 minimization method gives satisfactory results in sparse recovery no matter whether the measurement matrix is coherent or not.•For highly coherent measurements, the proposed method even outperforms the state-of-art ℓ1−ℓ2 minimization method.
The weighted ℓr−ℓ1 minimization method with 0<r≤1 largely generalizes the classical ℓr minimization method and achieves very good performance in compressive sensing. However, its restricted isometry property (RIP) and high-order RIP analysis results remain unknown. In this paper, we fill in this gap by adopting newly developed analysis tools. Moreover, through a novel decomposition of the objective function into a difference of two convex functions, we propose to solve the weighted ℓr−ℓ1 minimization problem via the difference of convex functions algorithms (DCA) directly. Numerical experiments show that our DCA based weighted ℓr−ℓ1 minimization method gives satisfactory results in sparse recovery no matter whether the measurement matrix is coherent or not. For highly coherent measurements, our proposed method even outperforms the state-of-art ℓ1−ℓ2 minimization method. |
| ArticleNumber | 108754 |
| Author | Zhou, Zhiyong |
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| DOI | 10.1016/j.sigpro.2022.108754 |
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| Keywords | Compressive sensing Restricted isometry property Difference of convex functions algorithms Nonconvex sparse recovery Weighted ℓr−ℓ1 minimization |
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| SubjectTerms | Compressive sensing Difference of convex functions algorithms Nonconvex sparse recovery Restricted isometry property Weighted [formula omitted] minimization |
| Title | RIP analysis for the weighted ℓr-ℓ1 minimization method |
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