Separable Joint Blind Deconvolution and Demixing

TL;DR

This paper introduces a separable convex optimization approach for blind deconvolution and demixing, improving computational efficiency while maintaining recovery guarantees, applicable to problems like blind MIMO.

Contribution

It proposes a novel separable formulation for blind deconvolution and demixing that reduces complexity without sacrificing recovery performance.

Findings

The method achieves accurate signal and kernel recovery.

It demonstrates improved computational efficiency over previous approaches.

Performance is validated under various normalization constraints.

Abstract

Blind deconvolution and demixing is the problem of reconstructing convolved signals and kernels from the sum of their convolutions. This problem arises in many applications, such as blind MIMO. This work presents a separable approach to blind deconvolution and demixing via convex optimization. Unlike previous works, our formulation allows separation into smaller optimization problems, which significantly improves complexity. We develop recovery guarantees, which comply with those of the original non-separable problem, and demonstrate the method performance under several normalization constraints.