A Triangle-Oriented Spatial-Temporal Phase Unwrapping Algorithm Based on Irrotational Constraints for Time-Series InSAR

The sparse 3-D phase unwrapping (PU) is a significant problem in the time-series interferometric synthetic aperture radar (TSInSAR), which is a popular technique on the extraction of the ground deformation. The popular 1-D + 2-D strategies in 3-D PU provide an initial temporal estimation of the phase gradients followed by a spatial integration procedure. However, the temporal PU (TPU) solution is prone to be spatially inconsistent, which increases the difficulty of the subsequent spatial PU (SPU). To solve the problem, in this article, an improved global TPU formulation targeting at a totally irrotational phase-gradient field is first proposed, which, however, has a heavy computation complexity, because numerous variables have to be optimized simultaneously. Consequently, a more feasible and practical triangle-oriented TPU (TOTPU) strategy is subsequently suggested, in which a triangle rather than an arc is the elementary unwrapping unit with the spatial irrotational constraints imposed. Furthermore, a residue-minimization algorithm is proposed to settle the problem of the “conflict edges” introduced by TOTPU, which occurs in just a small portion of arcs. Finally, the improved TPU phase gradients are integrated using an $L^{1}$ -norm SPU method with a novel weight function to obtain more reliable unwrapped phases. The proposed triangle-oriented spatial–temporal (TOST) algorithm is validated to be effective and reliable with both the simulated data and the real TerraSAR-X images. Moreover, it can be transplanted into a parallel platform for large-scale applications.