Abstract
In practical applications, some sparse signals have structural characteristics of block sparsity. Under the hypothesis of removing the requirements on the noise in recent literature concerning the \(\ell _2/\ell _p\,(0<p\le 1)\) minimization method, uniform block restricted isometry property (B-RIP) condition is established for the stable recovery of approximately block k-sparse signals with partial block support information by employing the weighted \(\ell _2/\ell _p\) minimization method. Compared with the state-of-the-art results, the newly-obtained results present more relaxed sufficient condition for block sparse signal recovery, and meanwhile provide more precise reconstruction error estimations in different noise settings. Numerical experiments demonstrate that the new method exhibits a substantial increase in the reconstruction quality for highly undersampled block structural signals.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grant number 12171496, in part by Guangdong Basic and Applied Basic Research Foundation under Grant number 2024A1515012057.
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Liu, W., Wan, A. Stable recovery of approximately block k-sparse signals with partial block support information via weighted \(\ell _2/\ell _p\,(0<p\le 1)\) minimization. Comp. Appl. Math. 43, 185 (2024). https://doi.org/10.1007/s40314-024-02714-6
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DOI: https://doi.org/10.1007/s40314-024-02714-6
Keywords
- Compressed sensing
- Approximately block k-sparse signal
- Stable recovery
- Weighted \(\ell _2/\ell _p\) minimization
- Block restricted isometry property