摘要
稀疏重构理论突破了传统信号处理的限制,为信息获取提供了新范式,在图像处理、通信系统等领域具有广泛的应用。其中,作为信号重构领域中一类新型的非凸正则化方法,误差函数(ERF)模型受到了广泛关注。为了研究不同权重对重构信号稀疏性的影响,从误差函数性质与稀疏重构理论出发,提出了一种结合自适应权重项与缩放ERF函数的新型正则化模型。证明了ERF函数在小信号值区域呈近似线性增长、大信号值区域趋于平缓的性质,具有在保持信号稀疏性的同时避免对大系数的过度惩罚的优点。借助加权误差函数模型的广义零空间性质,从理论上证明了新型正则化模型的优化问题能唯一重构s稀疏信号,为相关算法的实际应用提供了理论保障。
Sparse reconstruction theory overcomes the limitations of traditional signal processing,providing a new paradigm for information acquisition.It is widely applied in image processing and communication systems,etc.As a novel non-convex regularization method in signal reconstruction,the Error Function(ERF)model has garnered keen academic interest.To investigate the influence of different weights on sparse signal reconstruction,this paper proposes a new regularization model combining adaptive weight terms and scaled ERF functions based on error function properties and sparse reconstruction theory.First,the ERF function exhibits approximately linear growth in small signal value regions while tending to be gentle in large signal value regions.It maintains signal sparsity while avoiding excessive penalties on large coefficients.Through utilizing the generalized null space property of the weighted error function model,this novel regularization model reconstructs s sparse signals,providing a theoretical basis for the applications of related algorithms.
作者
谢挺
张艺萍
XIE Ting;ZHANG Yiping(Science of Mathematics College,Chongqing University of Technology,Chongqing 400054,China)
出处
《重庆理工大学学报(自然科学)》
北大核心
2025年第8期198-204,共7页
Journal of Chongqing University of Technology:Natural Science
基金
重庆市自然科学基金创新发展联合基金项目(CSTB2024NSCQ-LZX0093)
重庆市技术创新与应用发展专项重点项目(CSTB2022TIAD-KPX0100)
重庆市教委科技项目(KJZD-K202501104)。
关键词
压缩感知
稀疏重构
误差函数
零空间
compressed sensing
sparse reconstruction
error function
null space property
