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\(\mathrm {L_1RIP}\)-Based Robust Compressed Sensing

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Abstract

In the process of compressed sensing, environmental interference or various other factors can cause some of the information obtained by sampling to be abnormal. For this reason, the sparsity estimation of the signal will deviate from the real value, and the accuracy of signal recovery will decrease sharply. To solve this problem, a restricted isometry principle based on the \(\mathrm {L_1}\) norm (\(\mathrm {L_1RIP}\)) is proposed, which can be used as a basis for signal sparsity estimation. When the sensing matrix satisfies the \(\mathrm {L_1RIP}\), the sparsity of the signal can be accurately and stably estimated while preserving all of the measurement information even if there are outliers in the measurement vector. This paper also proposes an estimation method for the \(\mathrm {L_1RIP}\) constant. When the measurement matrix meets the \(\mathrm {L_1RIP}\) criterion under the constant obtained by this estimation method, the signal can be accurately reconstructed. The sparsity estimation method based on \(\mathrm {L_1RIP}\) is more robust and thereby improves the accuracy of signal recovery.

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Authors and Affiliations

  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China

    X. Gao & J. Zhou

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  2. J. Zhou
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Correspondence to J. Zhou.

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This work was supported in part by Chinese NSFC (Grant No. 62073023).

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Gao, X., Zhou, J. \(\mathrm {L_1RIP}\)-Based Robust Compressed Sensing. Circuits Syst Signal Process 41, 851–866 (2022). https://doi.org/10.1007/s00034-021-01805-7

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  • DOI: https://doi.org/10.1007/s00034-021-01805-7

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