合肥工业大学校徽

合肥工业大学学报自科版

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

主管：中华人民共和国教育部

主办：合肥工业大学

ISSN 1003-5060, CN 34-1083/N

基于同伦临近映射算法的低秩矩阵恢复

Low-rank matrix recovery based on homotopy proximity mapping algorithm

期刊信息

合肥工业大学（自然科学版），2025年8月，第48卷第8期：1106-1111

DOI: 10.3969/j.issn.1003-5060.2025.08.015

作者信息

班书宇，黄尉

（合肥工业大学数学学院，安徽合肥230601）

摘要和关键词

摘要: 文章提出的同伦临近映射（homotopy proximity mapping，HPM）算法可用于从信号的（噪声）线性测量中重建低秩信号或从观测数据中学习低秩线性模型。该算法在每次迭代时采用核范数的简单临近映射，并逐渐减小核范数的正则化参数。结果表明，HPM算法可在有噪测量下进行低秩矩阵恢复，且恢复结果表现为全局线性收敛。此外，更大的观测值可使HPM算法恢复更准确、收敛更快。

关键词: 压缩感知；矩阵恢复；同伦临近映射（HPM）；线性收敛

Authors

BAN Shuyu, HUANG Wei

(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: In this paper, a homotopy proximity mapping (HPM) algorithm is proposed to reconstruct low-rank signals from noisy linear measurements of signals or to learn low-rank linear models from observed data. The algorithm adopts a simple proximity mapping of the kernel norm during each iteration, and gradually reduces the regularization parameters of the kernel norm. The experimental results show that HPM algorithm can perform low-rank matrix recovery under noisy measurements, and the recovery results exhibit global linear convergence. In addition, increasing observation values leads to not only more accurate recovery, but also faster convergence.

Keywords: compressed sensing; matrix recovery; homotopy proximity mapping (HPM); linear convergence

基金信息

国家自然科学基金资助项目（62173121）

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