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arXiv · 1901.03041

A Unified Framework of State Evolution for Message-Passing Algorithms

Keigo Takeuchi
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Abstract

This paper presents a unified framework to understand the dynamics of message-passing algorithms in compressed sensing. State evolution is rigorously analyzed for a general error model that contains the error model of approximate message-passing (AMP), as well as that of orthogonal AMP. As a by-product, AMP is proved to converge asymptotically if the sensing matrix is orthogonally invariant and if the moment sequence of its asymptotic singular-value distribution coincide with that of the Marchenko-Pastur distribution up to the order that is at most twice as large as the maximum number of iterations.

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Keigo Takeuchi. 2019-01-10. A Unified Framework of State Evolution for Message-Passing Algorithms. https://arxiv.org/abs/1901.03041

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