Approximate Message Passing With Unitary Transformation for Robust Bilinear Recovery
Zhengdao Yuan, Qinghua Guo, Man Luo
Abstract
Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model Y = Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k=1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sup> b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> C + W, where {b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> } and C are jointly recovered with known Ak from the noisy measurements Y . The bilinear recovery problem has many applications such as dictionary learning, self-calibration, compressive sensing with matrix uncertainty, etc. In this work, we propose a new approximate Bayesian inference algorithm for bilinear recovery, where AMP with unitary transformation (UTAMP) is integrated with belief propagation (BP), variational inference (VI) and expectation propagation (EP) to achieve efficient approximate inference. It is shown that, compared to state-of-the-art bilinear recovery algorithms, the proposed algorithm is much more robust and faster, leading to remarkably better performance.