Very loopy belief propagation for unwrapping phase images

Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

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Brendan J. Frey, Ralf Koetter, Nemanja Petrovic


Since the discovery that the best error-correcting decoding algo(cid:173) rithm can be viewed as belief propagation in a cycle-bound graph, researchers have been trying to determine under what circum(cid:173) stances "loopy belief propagation" is effective for probabilistic infer(cid:173) ence. 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 imag(cid:173) ing techniques, including magnetic resonance imaging and interfer(cid:173) ometric 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.