基于IFISTA算法的LFM信号压缩感知重构  

LFM signal compressed sensing reconstruction based on improved fast iterative shrinkage⁃thresholding algorithm

作　　者：张瑞 孟晨 王成 王强 ZHANG Rui;MENG Chen;WANG Cheng;WANG Qiang(Department of Missilery Engineering,Shijiazhuang Campus of Army Engineering University of PLA,Shijiazhuang 050003,China)

机构地区：[1]陆军工程大学石家庄校区导弹工程系,河北石家庄050003

出　　处：《现代电子技术》2022年第11期11-17,共7页Modern Electronics Technique

基　　金：国家自然科学基金(61501493)资助课题。

摘　　要：快速迭代收缩阈值算法(FISTA)为低复杂度、高效率的信号重建铺平了道路。但是,当应用到线性调频信号重构时,传统的FISTA算法存在重构效果不佳、收敛速度慢等缺点。为了提高重建效果,提出基于保护系数的改进快速迭代收缩阈值算法(IFISTA)。在新方案下,首先,利用线性调频信号在分数阶傅里叶变换下的时频稀疏特性得到线性调频信号良好的稀疏表示,在迭代过程中对所有重构系数进行分析;然后,与特征相关的系数将被保护免受阈值收缩,以减少信息损失。仿真信号实验分析验证了该算法的有效性,结果表明,在相同信噪比条件下,提出的算法在线性调频信号的重构方面优于传统算法的性能。The fast iterative shrinkage⁃thresholding algorithm(FISTA)paves the way for low⁃complexity and high⁃efficiency signal reconstruction.However,when it is applied to the reconstruction of LFM(linear frequency modulation)signals,the traditional FISTA algorithm will generate disadvantages of poor reconstruction effect and slow convergence speed.Therefore,an improved fast iterative shrinkage⁃thresholding algorithm(IFISTA)based on protection coefficients is proposed to improve the reconstruction effect.In the new scheme,the LFM signal′s good sparse representation is obtained by the time⁃frequency sparse characteristics of the LFM signal under the fractional Fourier transform,and all reconstruction coefficients are analyzed in the iterative process.The coefficients related to the feature will be protected from threshold shrinkage to reduce information loss.The experiment analysis of the simulation signal has verified the effectiveness of the algorithm.The results show that,in the case of the same signal⁃to⁃noise ratio,the reconstruction of LFM signal of the proposed algorithm is better than that of the traditional algorithms.

关 键 词：线性调频信号 快速迭代收缩阈值算法 分数阶傅里叶变换 压缩感知 重构算法 稀疏表示 保护系数 

分 类 号：TN911.7-34[电子电信—通信与信息系统]