Large-Scale L ⁰ -Norm and L ¹ -Norm 2-D Phase Unwrapping

Two-dimensional phase unwrapping (PU) is a crucial processing step of synthetic aperture radar interferometry (InSAR). With the rapid advance of InSAR technology, the scale of interferograms is becoming increasingly larger. When the size of the input interferogram exceeds computer hardware capabilities, PU becomes more problematic in terms of computational and memory requirements. In the case of “big-data” PU, the input interferogram needs to be first tiled into a number of subinterferograms, unwrapped separately, and then spliced together. Hence, whether the PU result of each subinterferogram is consistent with that of the whole interferogram is critical to the large-scale PU process. To effectively solve this problem, the L1-norm envelope-sparsity theorem, which gives a sufficient condition to exactly guarantee the consistency between local and global L1-norm PU solutions, is put forward and proved. Furthermore, the L0-norm envelope-sparsity theorem, which gives a sufficient condition to exactly guarantee the consistency between local and global L0-norm PU solutions, is also proposed and proved. Afterward, based on these two theorems, two tiling strategies are put forward for the large-scale L0-norm and L1-norm PU methods. In addition, this paper presents the concepts of the tiling accuracy and the tiling resolution, which are the criteria used to evaluate the effectiveness of a tiling strategy, and we use them to quantitatively analyze the aforementioned tiling strategies. Both theoretical analysis and experimental results show that the proposed tiling strategies are effective for the largescale L0-norm and L1-norm PU problems.