一种基于STFT幅度测量值的图像相位恢复算法

Image Phase Recovery Algorithm Based on STFT Magnitude Measurement

图像相位恢复是指通过不含任何相位信息的幅度测量值恢复原始图像相位的问题.针对实际图像观测和传递过程中相位信息受到损失或者丢失的问题,利用原始图像短时傅里叶(Short-Time Fourier Transform,STFT)幅度测量值的唯一性,提出了一种图像相位恢复算法.通过改进的最小二乘法(Least Squares,LS)获取梯度下降法(GD,Gradient Descent)的迭代初始值,最小化构造非凸损失函数,解决了图像相位恢复的非凸优化问题.实验仿真中,在不同噪声类型和噪声强度的干扰下,相位恢复后的图像轮廓条纹依然清晰.实验结果表明,本文算法能够根据STFT幅度测量值恢复出图像的相位,具有较强的鲁棒性.

Image phase retrieval is the problem of recovering the original image phase from a Short-time Fourier Transform(STFT)measurement without any phase information.Regarding the problem of phase information loss of an image during the practical image observation and transmission,an algorithm based on the image restoring uniqueness of short-time Fourier transform magnitude measurement is proposed.In this algorithm,an iterative initial value of the gradient descent method obtained by the improved least squares(LS)method is minimizing a non-convex loss function.Then the algorithm could solve the problem of non-convex optimization of phase retrieval on image.In the experiment,under the interference of different noise types and intensity,the contour of the recovered image is still clear.Experimental results show that the algorithm can recover the original phase from STFT measurement and strong robustness.