基于分数函数LASSO最小化的稀疏性  

Sparsity Minimization Based on Fractional Function LASSO

作　　者：朱智慧 王会敏 孙兆颖 ZHU Zhihui;WANG Huimin;SUN Zhaoying(School of Mathematics,Physics and Information Science,Shaoxing University,Shaoxing,Zhejiang 312000)

机构地区：[1]绍兴文理学院数理信息学院,浙江绍兴312000

出　　处：《绍兴文理学院学报》2024年第8期63-71,共9页Journal of Shaoxing University

基　　金：国家自然科学基金面上项目“球面大数据建模研究的半监督梯度法”(61877039)。

摘　　要：压缩感知理论表明稀疏信号可以从欠定线性系统中精确重构,进而使得压缩感知理论广泛应用于各个方面。如何重构稀疏信号是压缩感知的核心问题。本文主要针对分数函数型的LASSO最小化进行研究,得出如果其数据是k-可压缩的,则分数函数型的LASSO最小化的最优解的稀疏性不超过[(1+δ)(β_(δ)+α/φ_(λ))^(2)k]。此外,也对最优解xλ和原始信号的近似解x(k)的l_(2)/l_(1)误差界进行了讨论,得出其误差界对参数k和λ的依赖程度。该结果可以为非凸压缩感知的理论研究提供一些参考。Compressed sensing theory shows that sparse signals can be accurately reconstructed from underdetermined linear systems,which makes compressed sensing theory widely used in various aspects.How to reconstruct sparse signals is the core problem of compressed sensing.In this paper,the minimization of LASSO of fractional function is mainly studied,and it is concluded that if its data is k-compressible,the sparsity of the optimal solution of LASSO minimization of fractional function does not exceed [(1+δ)(β_(δ)+α/φ_(λ))^(2)k].In addition,the L_(2)/L_(1) error bounds of the optimal solution xλand the approximate solution of the original signal x(k)are also discussed,and the degree to which the error bounds are dependent on the parameters k andλare generated.The results of this paper can provide some references for the theoretical research of non-convex compressed sensing.

关 键 词：压缩感知 稀疏信号 观测矩阵 LASSO最小化 

分 类 号：O24[理学—计算数学]