Esch, Christina: Development of a one-step three dimensional approach for the phase unwrapping process in a differential InSAR stack based on Small BAseline Subset (SBAS) interferograms. - Bonn, 2020. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
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author = {{Christina Esch}},
title = {Development of a one-step three dimensional approach for the phase unwrapping process in a differential InSAR stack based on Small BAseline Subset (SBAS) interferograms},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2020,
month = aug,

note = {Differential Interferometric Synthetic Aperture Radar (D-InSAR) is a unique technique to detect and map deformations of the Earth's surface over large temporal and spatial scales. Processing a whole stack of multitemporal data allows the generation of multidimensional deformation time series. One of the most important and critical steps in the analysis is the determination of phase ambiguities which is called phase unwrapping. The development of the phase unwrapping step in the context of the Small BAseline Subset (SBAS) method to analyze interferograms is the main focus of this work. In addition to the Permanent Scatterer Interferometry (PSI), the SBAS method is one of the most widely used methods for the multitemporal analysis of a D-InSAR stack. The SBAS method is especially suitable for noisy data because it provides a spatially more dense result. State of the art in the SBAS analysis is the Minimum Cost Flow (MCF) algorithm to spatially unwrap one single interferogram and the extended MCF (EMCF) algorithm to multitemporally unwrap a D-InSAR stack in two steps. Therefore, the problem is divided into two problems of smaller dimension, the temporal and the spatial phase unwrapping, which in turn can be solved as a two dimensional MCF problem. The MCF problem can be defined as a Linear Program (LP). The first contribution of this thesis is based on a detailed and consistent overview and discussion of the different formulations and solution methods of the MCF problem in order to find the most efficient solution for the problem in the context of SBAS.
Methodologically, the two-step algorithm is not optimal as the spatial phase unwrapping which follows in the second step destroys the temporal constraints which are fulfilled after the temporal phase unwrapping. So the goal of this thesis is the development of a one-step three dimensional approach. The number of papers that solve the phase unwrapping multitemporally in one step with help of the MCF problem is limited. Existing theoretical considerations and basic frameworks have not been resulting in an optimal solution. In particular the problem of temporal inconsistency, which occurs with spatially filtered so called multilooked interferograms, remains unsolved. The spatial filter is of particular importance especially with noisy data as it reduces the noise and makes phase unwrapping easier.
The second contribution of this thesis provides analysis and further refinements of the two-step EMCF algorithm. Based on these results a multitemporal one-step phase unwrapping procedure is finally developed. This approach is specifically designed for multilooked and multitemporally filtered SBAS interferograms. Both, simulated and real data are used to validate this approach. The test region is the Lower-Rhine-Embayment in the southwest of North Rhine-Westphalia, Germany, a very rural region with noisy data. Thus, there are only very few stable scatterers that can be evaluated. However, this region requires regular monitoring observations since one of the largest brown coal occurrences in Europe within this area leads to continuous movements of the Earth's surface. This work shows that the new approach provides more consistent results so that the deformation time series of the analyzed pixels can be improved. The performed simulations also demonstrate that the new approach leads to an improvement, especially in the case of very noisy data. In conclusion, using the methods developed in this work besides the stable scatterers, distributed scatterers can also be included in the analysis leading to a spatially increased density of the deformation time series.},

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