A novel approach for redundant integration of finite differences and phase unwrapping on a sparse multidimensional domain

Phase unwrapping and integration of finite differences are key problems in several technical fields, among which SAR interferometry. In this paper we propose a general formulation for robust and efficient integration of finite differences and for phase unwrapping, which includes standard techniques methods as sub-cases. The proposed approach allows obtaining more reliable and accurate solutions by exploiting redundant differential estimates (not only between nearest neighboring points) and multi-dimensional information (e.g. multitemporal, multi-frequency, multi-baseline), or external data (e.g. GPS measurements). The method requires the solution of linear or quadratic programming problems, for which computationally efficient algorithms exist. The validation tests performed confirm the validity of the technique.