Large-Scale Multibaseline Phase Unwrapping: Interferogram Segmentation Based on Multibaseline Envelope-Sparsity Theorem

Multibaseline (MB) phase unwrapping (PU) is a critical processing step for the MB synthetic aperture radar interferometry (InSAR). Compared with the traditional single-baseline (SB) PU, MB PU has wider application scope on the study area with strong phase variation, because it can overcome the limitation of the Itoh condition. Since most of the MB PU methods need to process multiple interferograms simultaneously, the size of the input interferograms will pose unique challenges when it exceeds the limit of computational capabilities. Until now, the research achievements related to large-scale (LS) MB PU have been quite limited. To deal with such case, we propose a technique for applying the two-stage programming-based MB PU method (TSPA) proposed by Yu and Lan to the LS MB InSAR data set in this paper. To be specific, the MB L-k-norm envelope-sparsity theorem is proposed and proved first, which gives a sufficient condition to exactly guarantee the consistency between local and global TSPA solutions. Afterward, based on the MB L-k-norm envelope-sparsity theorem, we put forward an interferogram tiling strategy, whereby each LS interferogram in the input MB InSAR data set is partitioned into a set of several smaller sub-interferograms that can be unwrapped individually by TSPA in parallel or in series. Both theoretical analysis and experimental results show that the proposed tiling strategy is effective for the LS MB PU problem.