Abstract
Phase unwrapping (PU) is a significant problem for reconstructing the deformation field during synthetic aperture radar interferometry analysis. The various 2-D PU algorithms can be divided into two categories: path-following methods and optimization-based methods. The former predefine an integration path in which the phase gradient is integrated to obtain the unwrapped results. The latter are path independent and error criterion oriented. The integration of the finite differences and the minimum cost flow solver describes a global optimization problem between the phase residues over closed spatial triangles computed over redundant neighboring edge sets. We propose a modified network using a simplified mathematical formulation for linear programming (LP) in the finite differences PU. Our algorithm has three major advantages over current methods. First, the modified network combines the Delaunay triangulation and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> nearest points to avoid isolated regions in the PU process. Second, modified formulation of the LP solver can directly obtain the phase ambiguity cycles of all points without integration. Finally, the combination of the new network and modified LP can achieve better PU results than the other state-of-the-art techniques. We applied our method to synthetic and real data from January 24, 2020 Mw 6.7 earthquake in Doğanyol–Sivrice, Turkey to August 8, 2017 Mw 6.5 earthquake in Jiuzhaigou, China. Comprehensive comparisons validate the effectiveness of our method.
Highlights
S YNTHETIC aperture radar interferometry has become a powerful tool in geophysics owing to its capability to derive spatially dense deformation maps with centimeter to millimeter accuracy [1], [2]
The L0-norm optimization model is commonly accepted as the best error criterion for Phase unwrapping (PU), as it keeps the phase gradient unchanged [12]; it cannot be solved in a polynomial time (NP-hard) [13]
For finite differences sparse PU (SPU), all edges are divided into two parts: the minimum spanning tree (MST) set and the edges in the remaining triangle loops
Summary
S YNTHETIC aperture radar interferometry has become a powerful tool in geophysics owing to its capability to derive spatially dense deformation maps with centimeter to millimeter accuracy [1], [2]. The L0-norm optimization model is commonly accepted as the best error criterion for PU, as it keeps the phase gradient unchanged [12]; it cannot be solved in a polynomial time (NP-hard) [13] In this context, minimum cost flow (MCF) based methods and minimum discontinuity methods [14] own the best optimization criterion for p = 1. In these methods, prior information is included when obtaining reliable unwrapped phase results. The objective of this article is to present a modification to finite differences SPU This method combines Delaunay triangulation and K neighboring edges to avoid isolated regions in the generated network. For the redundant edge network, the slack vectors for phase modulo of all points are introduced in the original MCF framework without changing the theoretical basis, and phase ambiguity can be directly obtained without integration through a fixed path.
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