Approximate Message Passing for Structured Affine Rank Minimization Problem
The topic of the rank minimization problem with affine constraints has been well studied in recent years. However, in many applications the data can exhibit other structures beyond simply being low rank. For example, images and videos present complex spatio-temporal structures, which are largely ign...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2017-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/7936453/ |
| _version_ | 1818853862520389632 |
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| author | Yangqing Li Changchuan Yin Wei Chen Zhu Han |
| author_facet | Yangqing Li Changchuan Yin Wei Chen Zhu Han |
| author_sort | Yangqing Li |
| collection | DOAJ |
| description | The topic of the rank minimization problem with affine constraints has been well studied in recent years. However, in many applications the data can exhibit other structures beyond simply being low rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current affine rank minimization (ARM) methods. In this paper, we propose a novel approximate message passing (AMP)-based approach that is capable of capturing additional structures in the matrix entries, and can be implemented in a wide range of applications with little or no modification. Using probabilistic low-rank factorization, we derive our generalized AMP-based algorithm as an approximation of the loopy belief propagation algorithm. In addition, we apply a rank selection strategy and an expectation-maximization estimation strategy that adaptively obtain the optimal value of the algorithmic parameters. Then, we discuss the specializations of our proposed algorithm to the applications of structured ARM problems, such as compressive hyperspectral imaging and compressive video surveillance. Simulation results with both synthetic and real data demonstrate that the proposed algorithm yields the state-of-the-art reconstruction performance while maintaining competitive computational complexity. |
| first_indexed | 2024-12-19T07:43:33Z |
| format | Article |
| id | doaj.art-3f0fa652d4444fcf81b59e98d8c0db2c |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-19T07:43:33Z |
| publishDate | 2017-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-3f0fa652d4444fcf81b59e98d8c0db2c2022-12-21T20:30:24ZengIEEEIEEE Access2169-35362017-01-015100931010710.1109/ACCESS.2017.27101797936453Approximate Message Passing for Structured Affine Rank Minimization ProblemYangqing Li0https://orcid.org/0000-0002-2272-4312Changchuan Yin1Wei Chen2Zhu Han3Beijing Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing, ChinaBeijing Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing, ChinaState Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, ChinaElectrical and Computer Engineering Department, University of Houston, Houston, TX, USAThe topic of the rank minimization problem with affine constraints has been well studied in recent years. However, in many applications the data can exhibit other structures beyond simply being low rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current affine rank minimization (ARM) methods. In this paper, we propose a novel approximate message passing (AMP)-based approach that is capable of capturing additional structures in the matrix entries, and can be implemented in a wide range of applications with little or no modification. Using probabilistic low-rank factorization, we derive our generalized AMP-based algorithm as an approximation of the loopy belief propagation algorithm. In addition, we apply a rank selection strategy and an expectation-maximization estimation strategy that adaptively obtain the optimal value of the algorithmic parameters. Then, we discuss the specializations of our proposed algorithm to the applications of structured ARM problems, such as compressive hyperspectral imaging and compressive video surveillance. Simulation results with both synthetic and real data demonstrate that the proposed algorithm yields the state-of-the-art reconstruction performance while maintaining competitive computational complexity.https://ieeexplore.ieee.org/document/7936453/Affine rank minimization (ARM)structured low-rank matrix recoveryapproximate message passing (AMP)belief propagationgraphical modelssum-product algorithm (SPA) |
| spellingShingle | Yangqing Li Changchuan Yin Wei Chen Zhu Han Approximate Message Passing for Structured Affine Rank Minimization Problem IEEE Access Affine rank minimization (ARM) structured low-rank matrix recovery approximate message passing (AMP) belief propagation graphical models sum-product algorithm (SPA) |
| title | Approximate Message Passing for Structured Affine Rank Minimization Problem |
| title_full | Approximate Message Passing for Structured Affine Rank Minimization Problem |
| title_fullStr | Approximate Message Passing for Structured Affine Rank Minimization Problem |
| title_full_unstemmed | Approximate Message Passing for Structured Affine Rank Minimization Problem |
| title_short | Approximate Message Passing for Structured Affine Rank Minimization Problem |
| title_sort | approximate message passing for structured affine rank minimization problem |
| topic | Affine rank minimization (ARM) structured low-rank matrix recovery approximate message passing (AMP) belief propagation graphical models sum-product algorithm (SPA) |
| url | https://ieeexplore.ieee.org/document/7936453/ |
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