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。
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.
作者
班书宇
黄尉
BAN Shuyu;HUANG Wei(School of Mathematics,Hefei University of Technology,Hefei 230601,China)
出处
《合肥工业大学学报(自然科学版)》
北大核心
2025年第8期1106-1111,共6页
Journal of Hefei University of Technology:Natural Science
基金
国家自然科学基金资助项目(62173121)。
关键词
压缩感知
矩阵恢复
同伦临近映射(HPM)
线性收敛
compressed sensing
matrix recovery
homotopy proximity mapping(HPM)
linear convergence
作者简介
班书宇(1996-),男,山东临沭人,合肥工业大学硕士生;通信作者:黄尉(1977-),男,安徽太湖人,博士,合肥工业大学教授,硕士生导师,E-mail:whuang@hfut.edu.cn.
