## Edgelist phase unwrapping algorithm for time series InSAR analysis

JOSA A, Vol. 27, Issue 3, pp. 605-612 (2010)

http://dx.doi.org/10.1364/JOSAA.27.000605

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### Abstract

We present here a new integer programming formulation for phase unwrapping of multidimensional data. Phase unwrapping is a key problem in many coherent imaging systems, including time series synthetic aperture radar interferometry (InSAR), with two spatial and one temporal data dimensions. The minimum cost flow (MCF) [
IEEE Trans. Geosci. Remote Sens.
36, 813 (1998)
] phase unwrapping algorithm describes a global cost minimization problem involving flow between phase residues computed over closed loops. Here we replace closed loops by reliable edges as the basic construct, thus leading to the name “edgelist.” Our algorithm has several advantages over current methods—it simplifies the representation of multidimensional phase unwrapping, it incorporates data from external sources, such as GPS, where available to better constrain the unwrapped solution, and it treats regularly sampled or sparsely sampled data alike. It thus is particularly applicable to time series InSAR, where data are often irregularly spaced in time and individual interferograms can be corrupted with large decorrelated regions. We show that, similar to the MCF network problem, the edgelist formulation also exhibits total unimodularity, which enables us to solve the integer program problem by using efficient linear programming tools. We apply our method to a persistent scatterer-InSAR data set from the creeping section of the Central San Andreas Fault and find that the average creep rate of

© 2010 Optical Society of America

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(280.6730) Remote sensing and sensors : Synthetic aperture radar

(350.5030) Other areas of optics : Phase

(100.5088) Image processing : Phase unwrapping

**ToC Category:**

Image Processing

**History**

Original Manuscript: August 31, 2009

Manuscript Accepted: December 8, 2009

Published: February 26, 2010

**Citation**

A. Piyush Shanker and Howard Zebker, "Edgelist phase unwrapping algorithm for time series InSAR analysis," J. Opt. Soc. Am. A **27**, 605-612 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-3-605

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