Sparse signal recovery via minimax‐concave penalty and ‐norm loss function
In sparse signal recovery, to overcome the ‐norm sparse regularisation's disadvantages tendency of uniformly penalise the signal amplitude and underestimate the high‐amplitude components, a new algorithm based on a non‐convex minimax‐concave penalty is proposed, which can approximate the ‐norm...
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| Veröffentlicht in: | IET signal processing Jg. 12; H. 9; S. 1091 - 1098 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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01.12.2018
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| ISSN: | 1751-9675 |
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| Abstract | In sparse signal recovery, to overcome the ‐norm sparse regularisation's disadvantages tendency of uniformly penalise the signal amplitude and underestimate the high‐amplitude components, a new algorithm based on a non‐convex minimax‐concave penalty is proposed, which can approximate the ‐norm more accurately. Moreover, the authors employ the ‐norm loss function instead of the ‐norm for the residual error, as the ‐loss is less sensitive to the outliers in the measurements. To rise to the challenges introduced by the non‐convex non‐smooth problem, they first employ a smoothed strategy to approximate the ‐norm loss function, and then use the difference‐of‐convex algorithm framework to solve the non‐convex problem. They also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. The simulation result demonstrates the authors’ conclusions and indicates that the algorithm proposed in this study can obviously improve the reconstruction quality. |
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| AbstractList | In sparse signal recovery, to overcome the ‐norm sparse regularisation's disadvantages tendency of uniformly penalise the signal amplitude and underestimate the high‐amplitude components, a new algorithm based on a non‐convex minimax‐concave penalty is proposed, which can approximate the ‐norm more accurately. Moreover, the authors employ the ‐norm loss function instead of the ‐norm for the residual error, as the ‐loss is less sensitive to the outliers in the measurements. To rise to the challenges introduced by the non‐convex non‐smooth problem, they first employ a smoothed strategy to approximate the ‐norm loss function, and then use the difference‐of‐convex algorithm framework to solve the non‐convex problem. They also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. The simulation result demonstrates the authors’ conclusions and indicates that the algorithm proposed in this study can obviously improve the reconstruction quality. |
| Author | Sun, Yuli Chen, Hao Tao, Jinxu |
| Author_xml | – sequence: 1 givenname: Yuli surname: Sun fullname: Sun, Yuli organization: Department of Electronic Engineering and Information Science University of Science and Technology of China Hefei People's Republic of China – sequence: 2 givenname: Hao surname: Chen fullname: Chen, Hao organization: Department of Electronic Engineering and Information Science University of Science and Technology of China Hefei People's Republic of China – sequence: 3 givenname: Jinxu surname: Tao fullname: Tao, Jinxu organization: Department of Electronic Engineering and Information Science University of Science and Technology of China Hefei People's Republic of China |
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| CitedBy_id | crossref_primary_10_1016_j_sigpro_2019_107369 crossref_primary_10_1016_j_neucom_2019_08_035 crossref_primary_10_1049_iet_spr_2019_0365 crossref_primary_10_1016_j_dsp_2025_105404 crossref_primary_10_1007_s10898_021_01028_9 crossref_primary_10_1016_j_acha_2022_07_002 crossref_primary_10_1016_j_knosys_2022_108230 crossref_primary_10_1007_s10878_022_00847_0 |
| Cites_doi | 10.1109/TSP.2017.2711501 10.1109/ICASSP.2016.7472557 10.1007/s10107-012-0629-5 10.1049/iet-ipr.2011.0312 10.1109/TNNLS.2012.2197412 10.1109/TSP.2017.2669904 10.1137/110840364 10.1088/1674-1056/23/7/078703 10.1109/TSP.2016.2598316 10.1002/ima.22156 10.1002/ima.22097 10.1109/TIP.2007.891805 10.1145/2339530.2339672 10.1016/j.ejor.2014.11.031 10.1109/TIT.2005.862083 10.1137/090777761 10.1109/TCSII.2013.2296133 10.1109/TIP.2011.2162418 10.1007/s00041-008-9045-x 10.1007/s10915-014-9930-1 10.1137/080716542 10.1609/aaai.v27i1.8605 10.1109/TIP.2013.2277821 10.1109/TCI.2017.2744626 10.1007/s10589-017-9954-1 10.1137/080725891 10.1137/140952363 10.1109/JSTSP.2009.2039181 10.1007/s10898-011-9765-3 10.1007/s10479-004-5022-1 10.1137/14098435X 10.3150/12-BEJ452 10.1002/0471725250 |
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