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Volume 42, Issue 1
Stable Recovery of Sparsely Corrupted Signals Through Justice Pursuit De-Noising

Ningning Li, Wengu Chen & Huanmin Ge

DOI: 10.4208/jcm.2204-m2021-0333

J. Comp. Math., 42 (2024), pp. 271-288.

Published online: 2023-12

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  • Abstract

This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. We provide new restricted isometry property (RIP) analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising (JPDN) with an additional parameter. Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method. The proposed RIP condition improves the existing representative results. Numerical simulations are provided to verify the reliability of the JPDN model.

  • Keywords

Justice Pursuit De-Noising, Restricted isometry property, Corrupted compressed sensing, Signal recovery.

  • AMS Subject Headings

65F22, 68W25, 90C25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-271, author = {Li , NingningChen , Wengu and Ge , Huanmin}, title = {Stable Recovery of Sparsely Corrupted Signals Through Justice Pursuit De-Noising}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {42}, number = {1}, pages = {271--288}, abstract = {

This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. We provide new restricted isometry property (RIP) analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising (JPDN) with an additional parameter. Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method. The proposed RIP condition improves the existing representative results. Numerical simulations are provided to verify the reliability of the JPDN model.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2204-m2021-0333}, url = {http://global-sci.org/intro/article_detail/jcm/22160.html} }
TY - JOUR T1 - Stable Recovery of Sparsely Corrupted Signals Through Justice Pursuit De-Noising AU - Li , Ningning AU - Chen , Wengu AU - Ge , Huanmin JO - Journal of Computational Mathematics VL - 1 SP - 271 EP - 288 PY - 2023 DA - 2023/12 SN - 42 DO - http://doi.org/10.4208/jcm.2204-m2021-0333 UR - https://global-sci.org/intro/article_detail/jcm/22160.html KW - Justice Pursuit De-Noising, Restricted isometry property, Corrupted compressed sensing, Signal recovery. AB -

This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. We provide new restricted isometry property (RIP) analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising (JPDN) with an additional parameter. Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method. The proposed RIP condition improves the existing representative results. Numerical simulations are provided to verify the reliability of the JPDN model.

Ningning Li, Wengu Chen & Huanmin Ge. (2023). Stable Recovery of Sparsely Corrupted Signals Through Justice Pursuit De-Noising. Journal of Computational Mathematics. 42 (1). 271-288. doi:10.4208/jcm.2204-m2021-0333
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