Discontinuity Preserving Phase Unwrapping Using Graph Cuts

  • José M. Bioucas-Dias
  • Gonçalo Valadão
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)


We present a new algorithm for recovering the absolute phase from modulo-2π phase, the so-called phase unwrapping (PU) problem. PU arises as a key step in several imaging technologies, from which we emphasize interferometric synthetic aperture radar/sonar (InSAR/SAS), magnetic resonance imaging (MRI), and optical interferometry. We adopt a discrete energy minimization viewpoint, where the objective function is a first-order Markov random field. The minimization problem is dealt with via a binary iterative scheme, with each iteration step cast onto a graph cut based optimization problem. For convex clique potentials we provide an exact energy minimization algorithm; namely we solve exactly the PU classical L p norm, with p ≥ 1. For nonconvex clique potentials, it is well known that PU performance is particularly enhanced, namely, the discontinuity preserving ability; however the problem is NP-hard. Accordingly, we provide an approximate algorithm, which is a modified version of the first proposed one. For simplicity we call both algorithms PUMF, for Phase Unwrapping Max-Flow. The state-of-the-art competitiveness of PUMF is illustrated in a series of experiments.


IEEE Transaction Synthetic Aperture Radar Machine Intelligence Optical Society Approximate Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • José M. Bioucas-Dias
    • 1
  • Gonçalo Valadão
    • 1
  1. 1.Instituto de TelecomunicaçõesInstituto Superior TécnicoLisboaPortugal

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