基于黎曼优化的联合稀疏盲反卷积
Jointly Sparse Blind Deconvolution via Riemannian Optimization
AI总结：
针对盲反卷积中联合稀疏性利用的难题，本文提出促进联合稀疏性的优化问题，开发黎曼优化算法，建立理论保证并通过数值实验验证其可降低样本复杂度、提升恢复性能。
AI中文摘要：
盲反卷积已广泛应用于系统辨识与信号处理领域。联合稀疏性在实际场景中普遍存在，但有效利用该结构提升恢复性能仍是极具挑战性且尚未完全解决的问题。本文提出一个促进联合稀疏性的优化问题，并开发了一种黎曼优化算法以实现准确高效的求解。我们进一步建立了理论保证，刻画了估计误差与样本复杂度之间的非渐近关系，表明利用联合稀疏性可显著降低成功恢复所需的样本复杂度。数值实验验证了理论结果，并证明了所提方法的有效性。
英文摘要：
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.
