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Abstract:
Since the discovery that the best error-correcting decoding
algorithm can be viewed as belief propagation in a cycle-bound
graph, researchers have been trying to determine under what
circumstances ``loopy belief propagation'' is effective for
probabilistic inference. Despite several theoretical advances in
our understanding of loopy belief propagation, to our knowledge,
the only problem that has been solved using loopy belief
propagation is error-correcting decoding on Gaussian channels. We
propose a new representation for the two-dimensional phase
unwrapping problem, and we show that loopy belief propagation
produces results that are superior to existing techniques. This
is an important result, since many imaging techniques, including
magnetic resonance imaging and interferometric synthetic aperture
radar, produce phase-wrapped images. Interestingly, the graph
that we use has a very large number of very short cycles,
supporting evidence that a large minimum cycle length is not
needed for excellent results using belief propagation.
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