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...

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Veröffentlicht in:IEEE access Jg. 5; S. 10093 - 10107
Hauptverfasser: Li, Yangqing, Yin, Changchuan, Chen, Wei, Han, Zhu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Piscataway IEEE 2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Affine rank minimization (ARM)
Algorithms
approximate message passing (AMP)
Approximation algorithms
belief propagation
Complexity
graphical models
Hyperspectral imaging
Image reconstruction
Message passing
Minimization
Optimization
Probabilistic logic
Signal processing algorithms
Sparse matrices
structured low-rank matrix recovery
sum-product algorithm (SPA)
Video compression
ISSN:2169-3536, 2169-3536
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Zusammenfassung: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.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2017.2710179