Bilinear Recovery Using Adaptive Vector-AMP

Subrata Sarkar; Alyson K. Fletcher; Sundeep Rangan; Philip Schniter

doi:10.1109/TSP.2019.2916100

Bilinear Recovery Using Adaptive Vector-AMP

Subrata Sarkar, Alyson K. Fletcher, Sundeep Rangan, Philip Schniter

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problem of jointly recovering the vector b and the matrix C from noisy measurements Y = A(b)C + W, where A(·) is a known affine linear function of b(i.e., A(b)=A₀ + ∑_i=1^Q b_iA_i with known matrices A_i). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear Generalized Approximate Message Passing.

Original language	English (US)
Article number	8712432
Pages (from-to)	3383-3396
Number of pages	14
Journal	IEEE Transactions on Signal Processing
Volume	67
Issue number	13
DOIs	https://doi.org/10.1109/TSP.2019.2916100
State	Published - Jul 1 2019

Keywords

Approximate message passing
computed tomography
dictionary learning
expectation maximization
expectation propagation
self-calibration

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2019.2916100

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title = "Bilinear Recovery Using Adaptive Vector-AMP",

abstract = "We consider the problem of jointly recovering the vector b and the matrix C from noisy measurements Y = A(b)C + W, where A(·) is a known affine linear function of b(i.e., A(b)=A0 + ∑i=1Q biAi with known matrices Ai). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear Generalized Approximate Message Passing.",

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author = "Subrata Sarkar and Fletcher, {Alyson K.} and Sundeep Rangan and Philip Schniter",

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AU - Rangan, Sundeep

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N2 - We consider the problem of jointly recovering the vector b and the matrix C from noisy measurements Y = A(b)C + W, where A(·) is a known affine linear function of b(i.e., A(b)=A0 + ∑i=1Q biAi with known matrices Ai). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear Generalized Approximate Message Passing.

AB - We consider the problem of jointly recovering the vector b and the matrix C from noisy measurements Y = A(b)C + W, where A(·) is a known affine linear function of b(i.e., A(b)=A0 + ∑i=1Q biAi with known matrices Ai). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear Generalized Approximate Message Passing.

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KW - expectation maximization

KW - expectation propagation

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Bilinear Recovery Using Adaptive Vector-AMP

Abstract

Keywords

ASJC Scopus subject areas

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