采用STFT幅度值的长信号相位恢复算法

Phase Retrieval of Long Signal Based on STFT Measurements

针对以往基于短时傅里叶变换(STFT)幅度值的相位恢复(STFTMPR)算法仅能处理一组较短的信号,并且信号的STFT幅度测量值的长度只能是质数的情况,提出了一种基于STFT幅度值的长信号相位恢复(LS-STFTMPR)算法。把一组长信号变化成几组较短的数组信号,通过改进的最小二乘(LS)法获取梯度下降(GD)法的迭代初始值,然后最小化各数组信号的非凸损失函数,并最终收敛到全局最小值。实验结果表明,在恢复一组较长信号的时候,所提算法的性能明显优于STFTMPR算法,并且具有较强的抗噪声能力。

The phase recovery algorithm based on the magnitude of Short-Time Fourier Transform（STFT）called STFTMPR algorithm,can only process a relatively short set of signals,and the length of the magnitude of the signal can only be prime number.An algorithm of Phase Retrieval of Long Signal Based on STFT Magnitude Measurements（LS-STFTMPR） is presented.A group of long signals are divided into several sets of short array signals,and the iterative value of the Gradient Descent（GD） method is initialized by an improved Least Squares（LS） method,then the non-convex loss function is minimized to make it converge to the global minimum.The experimental results show that when recovering a group of relatively long signals,the performance of the LS-STFTMPR algorithm with a high noise-resistance capability is obviously better than that of STFTMPR algorithm.