Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm
The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular locations and values of the sparse outliers are not...
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| Format: | Article |
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MDPI AG
2020-10-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/20/21/6111 |
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| author | Anyong Qin Lina Xian Yongliang Yang Taiping Zhang Yuan Yan Tang |
| author_facet | Anyong Qin Lina Xian Yongliang Yang Taiping Zhang Yuan Yan Tang |
| author_sort | Anyong Qin |
| collection | DOAJ |
| description | The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular locations and values of the sparse outliers are not known. Thus, the conventional methods cannot separate the low-rank and sparse components completely, especially in the case of gross outliers or deficient observations. Therefore, in this study, we employ the minimum description length (MDL) principle and atomic norm for low-rank matrix recovery to overcome these limitations. First, we employ the atomic norm to find all the candidate atoms of low-rank and sparse terms, and then we minimize the description length of the model in order to select the appropriate atoms of low-rank and the sparse matrices, respectively. Our experimental analyses show that the proposed approach can obtain a higher success rate than the state-of-the-art methods, even when the number of observations is limited or the corruption ratio is high. Experimental results utilizing synthetic data and real sensing applications (high dynamic range imaging, background modeling, removing noise and shadows) demonstrate the effectiveness, robustness and efficiency of the proposed method. |
| first_indexed | 2024-03-10T15:18:27Z |
| format | Article |
| id | doaj.art-0d46848ddb074cdd856e6504c96a9cbe |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T15:18:27Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-0d46848ddb074cdd856e6504c96a9cbe2023-11-20T18:42:57ZengMDPI AGSensors1424-82202020-10-012021611110.3390/s20216111Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic NormAnyong Qin0Lina Xian1Yongliang Yang2Taiping Zhang3Yuan Yan Tang4School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaSchool of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaSchool of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaCollege of Computer Science, Chongqing University, Chongqing 400030, ChinaFaculty of Science and Technology, University of Macau, Macau 999078, ChinaThe recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular locations and values of the sparse outliers are not known. Thus, the conventional methods cannot separate the low-rank and sparse components completely, especially in the case of gross outliers or deficient observations. Therefore, in this study, we employ the minimum description length (MDL) principle and atomic norm for low-rank matrix recovery to overcome these limitations. First, we employ the atomic norm to find all the candidate atoms of low-rank and sparse terms, and then we minimize the description length of the model in order to select the appropriate atoms of low-rank and the sparse matrices, respectively. Our experimental analyses show that the proposed approach can obtain a higher success rate than the state-of-the-art methods, even when the number of observations is limited or the corruption ratio is high. Experimental results utilizing synthetic data and real sensing applications (high dynamic range imaging, background modeling, removing noise and shadows) demonstrate the effectiveness, robustness and efficiency of the proposed method.https://www.mdpi.com/1424-8220/20/21/6111atomic normlow-rank matrix recoveryminimum description length principlerobust principal components analysis |
| spellingShingle | Anyong Qin Lina Xian Yongliang Yang Taiping Zhang Yuan Yan Tang Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm Sensors atomic norm low-rank matrix recovery minimum description length principle robust principal components analysis |
| title | Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm |
| title_full | Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm |
| title_fullStr | Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm |
| title_full_unstemmed | Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm |
| title_short | Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm |
| title_sort | low rank matrix recovery from noise via an mdl framework based atomic norm |
| topic | atomic norm low-rank matrix recovery minimum description length principle robust principal components analysis |
| url | https://www.mdpi.com/1424-8220/20/21/6111 |
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