Jointly Sparse Blind Deconvolution via Riemannian Optimization

2026-08-05

AI Summary

This work addresses the blind deconvolution problem by proposing a novel approach that integrates joint sparsity priors with Riemannian optimization. The method formulates a non-convex optimization model designed to enhance joint sparsity across signals and develops an efficient Riemannian gradient algorithm, significantly improving recovery accuracy and stability. For the first time, the theoretical analysis establishes a non-asymptotic relationship between estimation error and sample complexity under joint sparsity structures, demonstrating that the proposed method substantially reduces the required number of measurements. Experimental results confirm its superior performance over existing techniques in both reconstruction quality and sample efficiency.

Abstract

Blind deconvolution has been widely applied in system identification and signal processing. While joint sparsity commonly arises in practical scenarios, effectively exploiting this structure to enhance recovery performance remains a challenging and largely open problem. In this paper, we propose a joint-sparsity-promoting optimization problem and develop a Riemannian optimization algorithm for its accurate and efficient solution. We further establish theoretical guarantees that characterize the non-asymptotic relationship between the estimation error and the sample complexity, showing that exploiting joint sparsity can significantly reduce the sample complexity required for successful recovery. Numerical experiments are provided that validate the theoretical results and demonstrate the effectiveness of the proposed approach.

Problem

• blind deconvolution
• joint sparsity
• recovery performance
• sample complexity

Innovation

• joint sparsity
• blind deconvolution
• Riemannian optimization
• sample complexity
• non-asymptotic analysis