Quadratic Message Passing for Generalized Quadratic Equations Model

TL;DR

This paper proposes a new algorithm, Quadratic Message passing (QMP), which has a complexity as low as $O(N^{3})$.

Abstract

For approximate inference in the generalized quadratic equations model, many state-of-the-art algorithms lack any prior knowledge of the target signal structure, exhibits slow convergence, and can not handle any analytic prior knowledge of the target signal structure. So, this paper proposes a new algorithm, Quadratic Message passing (QMP). QMP has a complexity as low as $O(N^{3})$. The SE derived for QMP can capture precisely the per-iteration behavior of the simulated algorithm. Simulation results confirm QMP outperforms many state-of-the-art algorithms.

Figures (11)

• Figure 1: A factor graph for explaining message passing rules
• Figure 2: The factor graph of QMP
• Figure 3: The Markov chain sequence: $m^{+, t}_{\mathsf{z}} \rightarrow z \rightarrow m^{-, t}_{\mathsf{z}}$.
• Figure 4: Per-iteration MSEs of WF and QMP.
• Figure 5: Per-iteration Microscopic variables at $v_{\mathsf{w}} = \frac{1}{255}$.