Memory AMP
Lei Liu, Shunqi Huang, Brian M. Kurkoski

TL;DR
This paper introduces Memory AMP (MAMP), a low-complexity, orthogonality-based iterative estimation framework that achieves Bayes-optimal performance for high-dimensional linear systems with diverse matrix ensembles.
Contribution
The paper proposes MAMP and BO-MAMP, which ensure asymptotic Gaussian errors and match the performance of high-complexity methods, with practical complexity comparable to AMP.
Findings
MAMP guarantees asymptotically IID Gaussian errors.
BO-MAMP achieves Bayes-optimal MSE predicted by the replica method.
State evolution of BO-MAMP converges to the same fixed point as BO-OAMP/VAMP.
Abstract
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable (e.g., perform poorly or even diverge) for other matrix ensembles, especially for ill-conditioned ones. To solve this issue, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear minimum mean square error (MMSE) estimator. This prevents OAMP/VAMP from being used in large-scale systems. To address the drawbacks of AMP and BO-OAMP/VAMP, this paper offers a memory AMP (MAMP) framework based on the orthogonality principle, which ensures that estimation errors in MAMP are asymptotically IID…
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Taxonomy
TopicsRadar Systems and Signal Processing · Target Tracking and Data Fusion in Sensor Networks · Advanced Adaptive Filtering Techniques
