文献类型：期刊文献

英文题名：Fast and provable simultaneous blind super-Resolution and demixing for point source signals via scaled gradient descent

作者：Chen, Jinchi[1];Xiang, Zeyu[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China

年份：2026

卷号：176

外文期刊名：DIGITAL SIGNAL PROCESSING

收录：;EI(收录号：20261120242972);WOS:【SCI-EXPANDED(收录号:WOS:001712755300001)】；

基金：The authors thank the anonymous reviewers and the Associate Editor for their constructive comments and valuable suggestions, which have significantly improved the quality and clarity of this work. The authors also express gratitude to Jinsheng Li for constructive comments during the preparation of this work, which has significantly improved its quality. Additionally, the authors thank Ke Wei and Xu Zhang for their valuable discussions. This work was partially supported by the National Key R&D Program of China (Grant No. 2021YFA1003300) .

语种：英文

外文关键词：low rank matrix recovery; scaled gradient descent; Simultaneous blind super-resolution and demixing

摘要：We study the problem of simultaneously recovering multiple point source signals from low-frequency observations of their superimposed convolutions, where the associated point spread functions (PSFs) are unknown. Exploiting the inherent low-dimensional structures of both the signals and the PSFs, we formulate this task as a structured low-rank matrix demixing problem. To solve it, we adapt and refine the scaled gradient descent (Scaled-GD) algorithm, incorporating novel convergence guarantees specifically designed for the demixing setting. Our theoretical analysis establishes that, when initialized spectrally, Scaled-GD converges linearly to the ground truth under mild incoherence assumptions-and crucially, its convergence rate is independent of the condition number of the underlying matrices. Numerical experiments further validate the method's effectiveness, demonstrating competitive recovery performance and significantly improved computational efficiency compared to state-of-the-art convex approaches.