基于KL不等式求解压缩感知问题
Solving Compressed Sensing Problem Based on Kurdyka-?ojasiewicz Inequality
DOI: 10.12677/AAM.2022.111054, PDF,    科研立项经费支持
作者: 孙静坤, 许 荻, 任咏红*：辽宁师范大学，辽宁 大连
关键词: KL性质；压缩感知；线搜索；KL Properties； Compressed Sensing； Line Search
摘要: 压缩感知问题在雷达探测、信号与图象处理、组合优化、金融等诸多领域中有着非常广泛的应用。本文将压缩感知问题在一定的条件下转化为等价的无约束问题。通过研究这类无约束问题的KL (Kurdyka-Łojasiewicz)性质，本文采用BB步长，应用相应的非单调线搜索的方法求解这类非线性函数的收敛性和线性收敛速率。
Abstract: Compression sensing problem is widely used in radar detection, signal and image processing, combination optimization, finance and many other fields. In this paper, the compressed sensing problem is transformed into an equivalent unconstrained problem under certain conditions. By studying the Kurdyka-Łojasiewicz (KL) properties of such unconstrained problems, we use BB steps to solve the linear convergence and linear convergence rate of such nonlinear functions.
文章引用：孙静坤, 许荻, 任咏红. 基于KL不等式求解压缩感知问题[J]. 应用数学进展, 2022, 11(1): 462-472. https://doi.org/10.12677/AAM.2022.111054

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