量化压缩感知中最优阈值算法的数据时间权衡  

Data-time tradeoffs for optimal k-thresholding algorithms in quantized compressed sensing

作　　者：徐加樑 赵云彬 Jialiang Xu;Yunbin Zhao

机构地区：[1]北京科技大学数理学院,北京100083 [2]深圳市大数据研究院深圳国际工业与应用数学中心,深圳518172

出　　处：《中国科学:数学》2025年第2期343-360,共18页Scientia Sinica:Mathematica

基　　金：国家自然科学基金(批准号:12301393,12071307和12471295);基本科研业务费(批准号:FRF-TP-22-103A1);河套深港科技创新合作区深圳园区项目(批准号:HZQSWS-KCCYB-2024016)资助项目。

摘　　要：松弛最优阈值算法是压缩感知中的一种新的阈值技术,用于从少量带噪线性测量中高效恢复稀疏信号,克服了传统硬阈值算法由于残差函数振荡导致的缺点.本文考虑一种新颖的数据时间权衡分析,以说明在任何固定恢复精度下,松弛最优阈值算法在压缩感知、量化压缩感知还原信号过程中测量数量和迭代次数之间的权衡.理论结果还给出在压缩感知、量化压缩感知中实现信号恢复所需要的有效测量阶数.最后,通过数字实验也展示了松弛最优阈值算法在稀疏重建问题中的数据时间权衡.Relaxed optimal k-thresholding(ROT)algorithms are designed as a new thresholding technique in compressed sensing to efficiently recover a k-sparse signal from a small number of noisy linear measurements,which overcome the shortcomings of traditional hard thresholding algorithms caused by the oscillation of the residual function.In this paper,we carry out a novel data-time tradeoff analysis to characterize the tradeoff between the number of measurements and the number of iterations under any fixed recovery accuracy for the relaxed optimal k-thresholding algorithms in quantized compressed sensing.Both the analysis and numerical results from synthetic signal recovery demonstrate the data-time tradeoffs of ROT algorithms in sparse reconstruction problems.Furthermore,the theory presents the order of the number of measurements required for successful recovery in compressed sensing,quantized compressed sensing,and corrupted sensing.

关 键 词：压缩感知 量化压缩感知 稀疏重建问题 松弛最优阈值算法 数据时间权衡 

分 类 号：O224[理学—运筹学与控制论]