Very loopy belief propagation for unwrapping phase images

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

Bibtex Metadata Paper

Authors

Brendan J. Frey, Ralf Koetter, Nemanja Petrovic

Abstract

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.