Probabilistic cost functions for network flow phase unwrapping

  • Carballo G
  • Fieguth P
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Abstract

The well-studied interferometric synthetic aperture radar (InSAR)
problem for digital elevation map generation involves the derivation of
topography from radar phase. The topography is a function of the full
phase, whereas the measured phase is known module 2π, necessitating
the process of recovering full phase values via phase unwrapping. This
mathematical process becomes difficult through the presence of noise and
phase discontinuities. The authors' research is motivated by recent
research that models phase unwrapping as a network flow minimization
problem. The cost function to be optimized is a weighted
L1-norm of the phase discontinuities. Determining these cost
weights is critical, yet past work in the literature does not reflect
the statistics of the unwrapping problem. The purpose of this paper is
to propose a new method to compute the flow weights from a theoretical
foundation. Specifically, they formulate phase unwrapping as a maximum
likelihood (ML) estimation problem, which they mathematically rewrite as
a network flow problem with a specific choice of weights. The approach
is based on estimating the probability of phase discontinuities, which
can be derived as a function of coherence and topographic slope from the
known statistical properties of SAR phase

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Authors

  • Gabriel F. Carballo

  • Paul W. Fieguth

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