发表机构
Université de Montréal（蒙特利尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种平移不变的瓦片式相位解缠方法，结合DCT和最小二乘在频域解缠，并通过残差加权多路径平均消除瓦片伪影，在合成和真实数据上达到或超越现有技术水平。
AI 中文摘要
相位解缠是干涉测量和相干成像中的关键步骤，其中感兴趣的物理量由仪器仅以模2π形式提供的相位所承载。二维情况下的难点在于区分由缠绕引起的跳变与由噪声、真实不连续性、欠采样或去相关所产生的跳变。空间域和频率域方法均已被广泛研究，各自具有对方所缺乏的优势；将两者结合的混合方案仍然稀少。我们提出了一种半全局的瓦片式策略，其中每个瓦片通过离散余弦变换（DCT）和Ghiglia等人的最小二乘（LS）形式在频率域中解缠，瓦片随后在空间上进行合并。解缠和噪声滤波被联合执行，这使原本不适定的逆问题得以正则化。误差被限制在其产生的瓦片内；通过平均网格的每一次平移以及正方形的对称性来去除瓦片伪影；并且该平均值由每次遍历留下的泊松残差加权，因此，瓦片边界落在不连续性上的遍历不会将其接缝强加于结果。在合成数据和真实数据上，针对来自四个不同家族的四种参考算法，并在六种互补指标下进行的实验表明，所提出的方法匹配或改进了现有技术水平。其中一种指标，即本文引入的校正循环重缠绕残差，不需要真值，因此可适用于真实采集数据。
英文摘要
Phase unwrapping is a key step in interferometric and coherent imaging, where the physical quantity of interest is carried by a phase that the instrument delivers only modulo 2*pi. The difficulty in two dimensions is to separate the jumps caused by wrapping from those produced by noise, by true discontinuities, by under-sampling or by decorrelation. Spatial-domain and frequency-domain methods have both been studied extensively, each with advantages the other lacks; hybrid schemes combining the two remain scarce. We propose a semi-global tile-based strategy in which every tile is unwrapped in the frequency domain, through the Discrete Cosine Transform (DCT) and the least squares (LS) formalism of Ghiglia et al., the tiles being merged spatially. Unwrapping and noise filtering are performed jointly, which regularizes an otherwise ill-posed inverse problem. An error stays confined to the tile in which it arose; the tiling artifacts are removed by averaging over every shift of the grid and over the symmetries of the square; and that average is weighted by the Poisson residual each pass leaves behind, so that a pass whose tile boundaries fell on a discontinuity does not impose its seam on the result. Experiments on synthetic and real data, against four reference algorithms from four distinct families and under six complementary metrics, show that the proposed method matches or improves on the state of the art. One of these metrics, a corrected cyclic re-wrap residual introduced here, needs no ground truth and therefore remains available on real acquisitions.
Comments16 pages, 7 figures, 2 tables. Preprint
