分数傅里叶域中的相位恢复问题  

Phase Retrieval Problem in Fractional Fourier Domain

作　　者：廖天河[1] 高穹[2] 崔远峰[3] 宋凯洋[1] 

机构地区：[1]信息工程大学数学物理系,河南郑州450001 [2]国防科学技术大学光电科学与工程学院,湖南长沙410073 [3]中国卫星海上测控部,江苏江阴214431

出　　处：《激光与光电子学进展》2010年第8期55-63,共9页Laser & Optoelectronics Progress

摘　　要：对离散分数傅里叶变换(DFRFT)框架下复值信号和复值图像相位恢复问题的研究现状进行了评述。首先讨论了基于Gerchberg-Saxton(G-S)算法和DFRFT级次多样性的并行和串行G-S算法,并针对二维复值图像和级次个数为3的情形进行了数值模拟。结果表明,当3个级次在关于1对称的意义下的间隔较大时,这两种算法都相当有效;串行G-S算法的整体性能优于并行G-S算法。其次,针对一维复信号的情形,研究了一种基于非线性最小二乘的算法。这种算法首先将问题转化为非线性最小二乘形式的最优化问题,然后采用Mor啨形式的Levenberg-Marquardt算法求解。基于一维复值信号任意两个级次的DFRFT振幅,本算法都能得到相当精确的相位;即使对振幅含有中等噪声的情况,所得结果也比较满意。Under the condition of the framework of discrete fractional Fourier transform（DFRFT）,the research on the phase retrieval problem of complex signals and images is reviewed.Firstly,based on the basic Gerchberg-Saxton（G-S） algorithm and the diversity of the DFRFT orders,a great number of numerical simulations are performed for the case of complex image and three DFRFT orders.The results indicate that when the difference of these orders is large,the two algorithms are quite efficient,and the whole performance of the serial version is better than the parallel one.Secondly,for the case of 1-D complex signal,an algorithm based on the non-linear least-squares is studied.This algorithm converts the original problem into the optimization of a non-linear least-squares,and then is solved by the Levenberg-Marquardt algorithm of Moré′s form.With two DFRFT amplitudes of arbitrary orders,the algorithm can reconstruct quite accurate phase distribution,and its performance for noisy amplitudes is also satisfying.

关 键 词：图像处理 相位恢复 离散分数傅里叶变换 并行/串行G-S算法 非线性最小二乘 

分 类 号：O438[机械工程—光学工程]