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Phase unwrapping via diversity and graph cuts

Bioucas-Dias, J. ; Valadão, G.

Phase unwrapping via diversity and graph cuts, Proc International Conf. on Systems, Signals and Image Processing - IWSSIP, Bratislava, Slovakia, Vol. ?, pp. ? - ?, June, 2008.

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Abstract
Many imaging techniques, e.g., interferometric synthetic
aperture radar, magnetic resonance imaging, diffraction tomography, yield interferometric phase images. For these
applications, the measurements are modulo-2p, where p is
the period, a certain real number, whereas the aimed information
is contained in the true phase value. The process of
inferring the phase from its wrapped modulo-2pivalues is
the so-called phase unwrapping (PU) problem. In this paper
we present a graph-cuts based PU technique that uses two
wrapped images, of the same scene, generated with different
periods p1, p2. This diversity information allows to reduce
the ambiguity effect of the wrapping modulo-2p operation,
and is extensible to more than two periods. To infer the original
data, we assume a first order Markov random field (MRF)
prior and a maximum a posteriori probability (MAP) optimization
viewpoint. The employed objective functionals have
nonconvex, sinusoidal, data fidelity terms and a non isotropic
total variation (TV) prior. This is an integer, nonconvex optimization
problem for which we apply a technique that yields
an exact, low order polynomial complexity, global solution.
At its core is a non iterative graph cuts based optimization
algorithm. As far as we know, all the few existing period
diversity capable PU techniques for images, are either far too
simplistic or employ simulated annealing, thus exponential
complexity in time, optimization algorithms