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Compressed Sensing with Frames and Sparsity in Levels Class

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Abstract

Recently, lots of studies demonstrated that the signals are not only sparse in some system (e.g. shearlets) but also reveal a certain structure such as sparsity in levels. Therefore, sampling strategy is designed as a variable subsampling strategy in order to use this extra structure, for example magnetic resonance imaging (MRI) and etc. In this paper, we investigate the uniform recovery guarantees on the signals which possess sparsity in levels with respect to a general dual frame. First, we prove that the stable and robust recovery is possible when the weighted \(l^{2} \)-robust null space property in levels is satisfied. Second, we establish sufficient conditions under which subsampled isometry satisfies the weighted \(l^{2} \)-robust null space property in levels.

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Acknowledgements

The authors would like to thank the editors and reviewers for their careful reading and helpful suggestions.

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  1. Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

    Chol-Guk Choe & Chol-Song Rim

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  1. Chol-Guk Choe
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Choe, CG., Rim, CS. Compressed Sensing with Frames and Sparsity in Levels Class. Acta Appl Math 194, 4 (2024). https://doi.org/10.1007/s10440-024-00684-9

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