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arXiv · 2005.14132

Approximate Message Passing with Unitary Transformation for Robust Bilinear Recovery

Zhengdao Yuan·Qinghua Guo·Man Luo
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Abstract

Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C} +\boldsymbol{W} $, where $\{b_k\}$ and $\boldsymbol{C}$ are jointly recovered with known $\boldsymbol{A}_k$ from the noisy measurements $\boldsymbol{Y}$. 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.

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Zhengdao Yuan, Qinghua Guo, Man Luo. 2020-05-28. Approximate Message Passing with Unitary Transformation for Robust Bilinear Recovery. https://doi.org/10.1109/tsp.2020.3044847

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