← 研踪 PaperTrailarXiv:2509.10834 · v2
Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval via Structured Low-Rank Tensor Recovery
首次提交 2025-09-13 22:54
版本更新 2026-11-04 06:43
雷达观测 2026-11-05 11:11
摘要
This paper studies the landscape of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Since the complicated sensing structure makes direct landscape analysis technically challenging, we introduce a tractable tensor sensing surrogate that preserves the essential low-rank structure. We first analyze its population risk, characterize the global landscape on the unit sphere, and establish local linear convergence of Riemannian gradient descent (RGD) under mild conditions. We then extend the analysis to tensor sensing under a tensor restricted isometry property (TRIP), establishing local geometric and RGD convergence guarantees, and quantify robustness to measurement noise. Our theoretical results are further supported by extensive numerical experiments. These findings offer insights into the optimization landscape of the surrogate tensor sensing problem, thereby providing guidance for studying and solving the original BDPR problem.
作者备注：Revised version; 30 pages, 6 figures, plus 31 pages of supplementary material
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-04 06:43 · 最新观测版本
Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval via Structured Low-Rank Tensor Recovery
This paper studies the landscape of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Since the complicated sensing structure makes direct landscape analysis technically challenging, we introduce a tractable tensor sensing surrogate that preserves the essential low-rank structure. We first analyze its population risk, characterize the global landscape on the unit sphere, and establish local linear convergence of Riemannian gradient descent (RGD) under mild conditions. We then extend the analysis to tensor sensing under a tensor restricted isometry property (TRIP), establishing local geometric and RGD convergence guarantees, and quantify robustness to measurement noise. Our theoretical results are further supported by extensive numerical experiments. These findings offer insights into the optimization landscape of the surrogate tensor sensing problem, thereby providing guidance for studying and solving the original BDPR problem.
查看此版本解读 →查看此版本原文 ↗