Generalized Bilinear Factorization via Hybrid Vector Message Passing

Generalized bilinear factorization (GBF), in which two matrices are recovered from noisy and typically compressed measurements of their product, arises in various applications such as blind channel-and-signal estimation, image completion, and compressed video foreground and background separation. In...

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Vydané v:	IEEE transactions on signal processing Ročník 72; s. 5675 - 5690
Hlavní autori:	Jiang, Hao, Yuan, Xiaojun, Guo, Qinghua
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms Approximation algorithms Background noise Closed form solutions Convergence Correlation Covariance matrices Damping Exact solutions expectation propagation Factorization Free energy Generalized bilinear factorization Inference algorithms Inverse problems Message passing Signal processing algorithms Sparse matrices variational free energy minimization variational message passing Vectors Video compression
ISSN:	1053-587X, 1941-0476
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Abstract	Generalized bilinear factorization (GBF), in which two matrices are recovered from noisy and typically compressed measurements of their product, arises in various applications such as blind channel-and-signal estimation, image completion, and compressed video foreground and background separation. In this paper, we formulate the GBF problem by unifying several existing bilinear inverse problems, and establish a novel hybrid vector message passing (HVMP) algorithm for GBF. The GBF-HVMP algorithm integrates expectation propagation (EP) and variational message passing (VMP) via variational free energy minimization, and exchanges matrix-variable messages in closed form. GBF-HVMP is advantageous over its counterparts in several aspects. For example, a matrix-variable message can characterize the correlations between the elements of the matrix, which is not possible in scalar-variable message passing; the hybrid of EP and VMP yields closed-form Gaussian messages associated with the bilinear constraints inherent in the GBF problem. We show that damping is unnecessary for GBF-HVMP to ensure convergence. We also show that GBF-HVMP performs close to the replica bound, and significantly outperforms state-of-the-art approaches in terms of both normalized mean squared error (NMSE) performance and computational complexity.
AbstractList	Generalized bilinear factorization (GBF), in which two matrices are recovered from noisy and typically compressed measurements of their product, arises in various applications such as blind channel-and-signal estimation, image completion, and compressed video foreground and background separation. In this paper, we formulate the GBF problem by unifying several existing bilinear inverse problems, and establish a novel hybrid vector message passing (HVMP) algorithm for GBF. The GBF-HVMP algorithm integrates expectation propagation (EP) and variational message passing (VMP) via variational free energy minimization, and exchanges matrix-variable messages in closed form. GBF-HVMP is advantageous over its counterparts in several aspects. For example, a matrix-variable message can characterize the correlations between the elements of the matrix, which is not possible in scalar-variable message passing; the hybrid of EP and VMP yields closed-form Gaussian messages associated with the bilinear constraints inherent in the GBF problem. We show that damping is unnecessary for GBF-HVMP to ensure convergence. We also show that GBF-HVMP performs close to the replica bound, and significantly outperforms state-of-the-art approaches in terms of both normalized mean squared error (NMSE) performance and computational complexity.
Author	Guo, Qinghua Jiang, Hao Yuan, Xiaojun
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SubjectTerms	Algorithms Approximation algorithms Background noise Closed form solutions Convergence Correlation Covariance matrices Damping Exact solutions expectation propagation Factorization Free energy Generalized bilinear factorization Inference algorithms Inverse problems Message passing Signal processing algorithms Sparse matrices variational free energy minimization variational message passing Vectors Video compression
Title	Generalized Bilinear Factorization via Hybrid Vector Message Passing
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