Limitations and Potentials of Quantum Computing for InSAR Phase Unwrapping

Phase unwrapping is the reconstruction of an absolute phase given its values modulo $2\pi$. This post-processing step is commonly used in synthetic aperture radar interferometry (InSAR) for applications such as estimating topographic height and surface deformation. Conventional InSAR unwrapping techniques are designed for large-scale phase correction, focusing on overall consistency and often relying on auxiliary data, such as additional acquisitions or ground data, to compensate for significant local height changes. Motivated by recent advances in quantum algorithms for optimisation and phase retrieval, we explore the potential of gate-based quantum computing and hybrid quantum approaches for addressing the phase unwrapping problem. We provide an overview of the fundamental and practical limitations of quantum computing, with particular emphasis on the constraints imposed by the current noisy intermediate-scale quantum era. Furthermore, we highlight three promising directions for improved phase unwrapping: accelerating existing $L^1$ optimisation methods, enabling direct access to $L^0$ formulations, and enhancing the performance of machine learning-based approaches.