Approximate Message Passing with Unitary Transformation for Robust Bilinear Recovery

Abstract

Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\mathbf{Y}={\sum }_{k=1}^K{b}_k{\mathbf{A}}_k\mathbf{C}+\mathbf{W}$, where $\{b_k\}$ and $\mathbf{C}$ are jointly recovered with known ${\mathbf{A}}_k$ from the noisy measurements $\mathbf{Y}$. The bilinear recover problem has many applications such as dictionary learning, self-calibration, compressive sensing with matrix uncertainty, etc. In this work, we propose a new bilinear recovery algorithm based on AMP with unitary transformation. It is shown that, compared to the state-of-the-art message passing based algorithms, the proposed algorithm is much more robust and faster, leading to remarkably better performance.

arXiv comment11 pages, 12 figures

References in corpus (12)

• Expectation Propagation for approximate Bayesian inference
• Expectation-Maximization Gaussian-Mixture Approximate Message Passing
• An overview of low-rank matrix recovery from incomplete observations
• Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling
• Self-Calibration and Biconvex Compressive Sensing
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• A Unified Bayesian Inference Framework for Generalized Linear Models
• A Generalized Mean Field Algorithm for Variational Inference in Exponential Families
• Parametric Bilinear Generalized Approximate Message Passing
• Approximate Message Passing with Unitary Transformation
• Low Complexity Sparse Bayesian Learning Using Combined BP and MF with a Stretched Factor Graph
• Bilinear Recovery using Adaptive Vector-AMP

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