Dias José M B, Leitao José M N
Instituto de Telecomunicacoes, Instituto Superior Tecnico, Lisbon, Portugal.
IEEE Trans Image Process. 2002;11(4):408-22. doi: 10.1109/TIP.2002.999675.
This paper presents an effective algorithm for absolute phase (not simply modulo-2-pi) estimation from incomplete, noisy and modulo-2pi observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2-pi-periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques and an iterative conditional modes (ICM) step (pi-step). Accordingly, the algorithm is termed ZpiM, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2pi-multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.
本文提出了一种有效的算法，用于从干涉孔径雷达和声纳（InSAR/InSAS）中不完整、有噪声且模2π的观测值中估计绝对相位（而非简单的模2π相位）。所采用的框架在其他应用中也具有代表性，如光学干涉测量、磁共振成像和衍射层析成像。本文采用贝叶斯观点；观测密度是2π周期的，并考虑了干涉对去相关和系统噪声；绝对相位的先验概率由针对分段平滑绝对相位图像定制的复合高斯 - 马尔可夫随机场（CGMRF）建模。我们提出了一种用于计算最大后验概率（MAP）绝对相位估计的迭代方案。每次迭代包含一个离散优化步骤（Z步），通过网络编程技术实现，以及一个迭代条件模式（ICM）步骤（π步）。因此，该算法被称为ZpiM，其中字母M代表最大化。本文的一个重要贡献是同时实现了相位解缠（推断2π的倍数）和平滑（观测值去噪）。与在解缠之前对数据进行低通滤波的方法相比，这大大提高了绝对相位估计的准确性。一组将所提出算法与其他方法进行比较的实验结果说明了我们方法的有效性。
