Unfolding Neural Networks for Compressive Multichannel Blind Deconvolution

TL;DR

This paper introduces a learned neural network approach for compressive multichannel blind deconvolution, jointly learning the source, sparse filters, and compression matrix in an unsupervised manner, with practical hardware implementation benefits.

Contribution

It proposes a novel autoencoder based on unfolding neural networks that learns the compression matrix and performs blind deconvolution without prior fixed compression schemes.

Findings

Outperforms classical methods in accuracy

Faster sparse filter recovery

Enables practical hardware implementation

Abstract

We propose a learned-structured unfolding neural network for the problem of compressive sparse multichannel blind-deconvolution. In this problem, each channel's measurements are given as convolution of a common source signal and sparse filter. Unlike prior works where the compression is achieved either through random projections or by applying a fixed structured compression matrix, this paper proposes to learn the compression matrix from data. Given the full measurements, the proposed network is trained in an unsupervised fashion to learn the source and estimate sparse filters. Then, given the estimated source, we learn a structured compression operator while optimizing for signal reconstruction and sparse filter recovery. The efficient structure of the compression allows its practical hardware implementation. The proposed neural network is an autoencoder constructed based on an unfolding approach: upon training, the encoder maps the compressed measurements into an estimate of sparse filters using the compression operator and the source, and the linear convolutional decoder reconstructs the full measurements. We demonstrate that our method is superior to classical structured compressive sparse multichannel blind-deconvolution methods in terms of accuracy and speed of sparse filter recovery.