Unrolled Compressed Blind-Deconvolution

TL;DR

This paper introduces a compression-based approach for sparse multichannel blind deconvolution that reduces measurement costs and employs a data-driven unrolled learning framework for improved robustness and generalization.

Contribution

It proposes a novel compression method with theoretical guarantees and an unrolled learning framework for blind deconvolution, enhancing efficiency and robustness.

Findings

Compression enables blind recovery from fewer measurements.

Unrolled learning outperforms optimization-based methods in robustness.

Superior generalization in data-limited scenarios.

Abstract

The problem of sparse multichannel blind deconvolution (S-MBD) arises frequently in many engineering applications such as radar/sonar/ultrasound imaging. To reduce its computational and implementation cost, we propose a compression method that enables blind recovery from much fewer measurements with respect to the full received signal in time. The proposed compression measures the signal through a filter followed by a subsampling, allowing for a significant reduction in implementation cost. We derive theoretical guarantees for the identifiability and recovery of a sparse filter from compressed measurements. Our results allow for the design of a wide class of compression filters. We, then, propose a data-driven unrolled learning framework to learn the compression filter and solve the S-MBD problem. The encoder is a recurrent inference network that maps compressed measurements into an estimate of sparse filters. We demonstrate that our unrolled learning method is more robust to choices of source shapes and has better recovery performance compared to optimization-based methods. Finally, in data-limited applications (fewshot learning), we highlight the superior generalization capability of unrolled learning compared to conventional deep learning.