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.

11 pages, 12 figures