Approximate Message Passing with Restricted Boltzmann Machine Priors

TL;DR

This paper enhances signal reconstruction in compressed sensing by integrating a hierarchical RBM prior into AMP, improving performance on signals with structured support, demonstrated on MNIST data.

Contribution

Introduces a hierarchical RBM prior into AMP for better support modeling, with analysis of RBM factorization effects and experimental validation on MNIST.

Findings

RBM prior improves AMP reconstruction performance.

RBM-based AMP approaches oracle-support accuracy.

Factorization methods influence reconstruction quality.

Abstract

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.