2019/05/10 by Yanting Ma, Ma, Yanting, Cynthia Rush +3
Computer Science · Engineering · #Blind Source Separation Techniques #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1905.03913
openalex publication_date 2019/05/10 · openalex created_date 2019/05/16 · openalex updated_date 2026/07/28
Approximate message passing (AMP) is a class of low-complexity, scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal from noisy, linear measurements. AMP is an iterative algorithm that performs estimation by updating an estimate of the unknown signal at each iteration and the performance of AMP (quantified, for example, by the mean squared error of its estimates) depends on the choice of a "denoiser" function that is used to produce these signal estimates at each iteration. An attractive feature of AMP is that its performance can be tracked by a scalar recursion referred to as state evolution. Previous theoretical analysis of the accuracy of the state evolution predictions has been limited to the use of only separable denoisers or block-separable denoisers, a class of denoisers that underperform when sophisticated dependencies exist between signal entries. Since signals with entrywise dependencies are common in image/video-processing applications, in this work we study the high-dimensional linear regression task when the dependence structure of the input signal is modeled by a Markov random field prior distribution. We provide a rigorous analysis of the performance of AMP, demonstrating the accuracy of the state evolution predictions, when a class of non-separable sliding-window denoisers is applied. Moreover, we provide numerical examples where AMP with sliding-window denoisers can successfully capture local dependencies in images.