Approximate Message Passing with Unitary Transformation for Robust Bilinear Recovery

TL;DR

This paper introduces a new approximate message passing algorithm with unitary transformation for bilinear recovery, demonstrating improved robustness and speed over existing methods in applications like dictionary learning and compressive sensing.

Contribution

The paper proposes a novel AMP-based bilinear recovery algorithm utilizing unitary transformation, enhancing robustness and computational efficiency.

Findings

Significantly improved robustness over existing algorithms.

Faster convergence and better performance in simulations.

Effective in applications like dictionary learning and compressive sensing.

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.