无网格压缩感知下结合傅里叶变换的FT-ANM算法  

FT-ANM Algorithm Combined with Fourier Transform in Gridless Compressive Sensing

作　　者：李慧启 李立春[1] 刘志鹏 LI Huiqi;LI Lichun;LIU Zhipeng(Information Engineering University, Zhengzhou 450001,China)

机构地区：[1]信息工程大学,河南郑州450001

出　　处：《信息工程大学学报》2018年第4期475-479,共5页Journal of Information Engineering University

摘　　要：为克服在无网格压缩感知理论中利用原子范数最小化(atomic norm minimization, ANM)算法进行线谱估计时存在的运算复杂度高,估计实时性不强等缺点,提出一种ANM的改进算法,傅里叶-原子范数最小化算法(fourier transform-atomic norm minimization,FT-ANM)。对ANM算法中前期取得的重构信号进行傅里叶变换,粗估计出重构信号的模型阶数,减少对拓普利兹矩阵进行Vandermonde分解时估计参数的数量,提高ANM算法的运算速率,增强线谱估计的实时性。仿真结果显示,在相同信噪比条件下,FT-ANM算法运算速率是传统ANM算法运算的3倍,运算复杂度低,实时性较好。To address high computational complexity and poor real-time estimation performance of atomic norm minimization (ANM) algorithm in gridless compressive sensing, a modified ANM algorithm,the Fourier transform-atomic norm minimization (FT-ANM) algorithm, is proposed. We firstly transform the reconstructed signal in the early stage of ANM algorithm into Fourier domain and then roughly estimate the model order of reconstructed signal. As a result, the number of estimated parameters decreases when the Toeplitz matrix is decomposed by Vandermonde theorem. The operation speed of ANM algorithm is improved and the real-time performance of line spectrum estimation also enhanced. Simulation results show that under the same condition of SNR, the computation speed of FT-ANM algorithm is about three times as fast as the ANM algorithm, with lower computational complexity and higher estimation performance.

关 键 词：无网格压缩感知 原子范数 线谱估计 Vandermonde分解 拓普利兹矩阵 

分 类 号：TN911.7[电子电信—通信与信息系统]