Approximate Message Passing with Unitary Transformation for Robust Bilinear Recovery

• Published in: arXiv.org
• Main Authors: Yuan, Zhengdao, Guo, Qinghua, Luo, Man
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.12.2020
• Subjects: Algorithms; Computer Science - Information Theory; Mathematics - Information Theory; Message passing; Recovery; Robustness; Self calibration
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2005.14132

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.