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Edgelist phase unwrapping algorithm for time series InSAR analysis.

A Piyush Shanker1, Howard Zebker

  • 1Department of Electrical Engineering, Stanford University, 350 Serra Mall, Packard 334, Stanford, California 94305, USA. shanker@stanford.edu

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A new edgelist formulation simplifies multidimensional phase unwrapping for synthetic aperture radar interferometry. This method improves accuracy by incorporating external data and efficiently solving complex problems.

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Area of Science:

  • Geophysics
  • Remote Sensing
  • Computer Science

Background:

  • Phase unwrapping is crucial for coherent imaging systems like time series synthetic aperture radar interferometry (InSAR).
  • Existing minimum cost flow (MCF) algorithms for phase unwrapping involve complex flow calculations over closed loops.
  • Multidimensional data and irregularly sampled time series InSAR present significant unwrapping challenges.

Purpose of the Study:

  • To introduce a novel integer programming formulation for multidimensional phase unwrapping.
  • To develop an 'edgelist' approach that simplifies phase unwrapping by using reliable edges instead of closed loops.
  • To enhance the applicability of phase unwrapping to complex datasets, including time series InSAR.

Main Methods:

  • Developed a new integer programming formulation for phase unwrapping based on an 'edgelist' construct.
  • Demonstrated that the edgelist formulation exhibits total unimodularity, allowing for efficient linear programming solutions.
  • Incorporated external data sources (e.g., GPS) to constrain the unwrapped phase solution.

Main Results:

  • The edgelist method simplifies multidimensional phase unwrapping and handles both regularly and sparsely sampled data.
  • Applied to a persistent scatterer-InSAR dataset from the San Andreas Fault, revealing detailed creep rate variations.
  • The analysis showed a constant average creep rate of 22 mm/Yr from 1992-2004, with spatial variations and a temporal trend.

Conclusions:

  • The edgelist formulation offers a more flexible and efficient approach to multidimensional phase unwrapping.
  • This method is particularly well-suited for time series InSAR data, even with temporal sampling irregularities and decorrelation.
  • The application to the San Andreas Fault demonstrates the potential for precise geodetic measurements using this technique.