InSAR Phase Unwrapping using Deep Learning

Given the importance of monitoring natural hazards, Interferometric Synthetic Aperture Radar (InSAR) has proven to be a powerful tool to monitor, at high spatial and temporal resolution, deformation across the Earth’s surface (Lazecký et al. 2020). Wrapped interferograms record phase as modulo 2π, introducing ambiguity in the relative displacement; thus phase unwrapping is required using
ϕ =ψ+2πk, (0.1)
where ϕ is unwrapped phase, ψ is wrapped phase and k is an integer wrap count value. Given the ill posed nature of phase unwrapping (Itoh 1982), generally it is assumed that the absolute difference in phase gradient between neighbouring pixels will not exceed π.

However, this is not always true; to identify residues, the summed difference of a 2x2 pixel square is calculated, and where not equal to 0 (Goldstein et al. 1988). During phase unwrapping, often the goal is to identify an optimal integration pathway, which minimises the difference between the wrapped and unwrapped phase gradients through an Lp norm optimisation (Ghiglia et al. 1996).
Phase unwrapping is most difficult in regions of high noise (Chen 2001) and where there has been insufficient sampling relative to the amount of deformation (Kester 2009) due to the high degree of uncertainty associated with the wrapped phase gradient and thus, within these regions, phase unwrapping errors are most likely to be introduced.

Phase unwrapping remains an active research field (Mu et al. 2023; Pepin et al. 2024; Zhou et al. 2022a). Recently, the focus has shifted to utilising deep learning models for phase unwrapping, particularly focused upon increasing phase unwrapping robustness in high phase noise regions and, given its importance to optimising the integration pathway, the correct identification of phase gradients (Sica et al. 2022; Wang et al. 2021). A popular approach is for trained models to classify phase gradients into 3 classes.

In this thesis, I present work which explores the use of deep learning to improve the unwrapped phase result by reducing phase unwrapping errors associated with large phase gradients, high phase noise and isolated regions of coherent pixels. This work builds upon previous publications proposals which classify gradients as 0 change, +1 or more and-1 or less wrap count difference. This does not allow the differentiation of absolute gradients exceeding 1 wrap count.

I begin by presenting a complete unwrapping approach called Multi-Class Greedy Phase Integrator (MC-GI). A semantic segmentation U-Net model is trained to include at least one additional phase gradient class to allow the explicit identification of larger gradients and a novel Greedy Phase Integrator is used to integrate the gradient maps, prioritising those gradients where the model has a high degree of certainty in its prediction. Though the MC-GI has good performance on synthetic interferograms, and interferograms with high fringe rates but low noise, the robustness of unwrapping in the presence of high noise was poor. Furthermore, the isolation of coherent regions led to local accuracy in the unwrapped phase result but global unwrapping errors overall due to an offset in wrap count between isolated regions.

I then present a Multi-Class Cost Guided Phase Integrator approach (MC-CGI) with the aim of improving robustness of unwrapping in high phase noise regions whilst retaining the advantage of identifying large phase gradients. I train a semantic segmentation model using a training data set which includes circular Gaussian noise. Gradient maps are integrated using the cost-guided optimisation method SNAPHU (Chen et al. 2001), where the wrap count gradient and model prediction certainty are used to inform the offset and variance respectively a priori. Results indicate an improved unwrapping performance for synthetic and real Sentinel-1 data, compared to applying SNAPHU alone. Whereas for synthetic data, a MC[4]-CGI (4 class) approach performed best, for real data, the success of the approach was not reliant on the number of classes chosen, with a 3 class, 4 class and 5 class model performing equally well.

To minimise the unwrapping error associated with isolation of coherent regions, I explore the impact of using a Brownian Bridge Diffusion Model (Bo et al. 2023) to gap fill masked regions with a realistic data distribution. Qualitatively, results for mainly atmospheric gaps are promising where few signals are associated with deformation, however either model fine-tuning or retraining using a data set containing signal examples of ringed
deformation, often associated with earthquakes, mountainous regions and volcanic deformation, is required to increase the generalisability of the BBDM. With respect to phase unwrapping, the gap filling does reduce the phase error associated with isolated regions, however it success is dependent on the signal type of signal and mask size, meaning whilst initial results are promising, further work is required to increase the methods reliability and generalisability.