|Stochastic Systems Group|
Professor Brendan Frey
University of Toronto
Since the discovery that the best error-correcting decoding algorithm can be viewed as probability propagation (a.k.a. the sum-product algorithm and belief propagation) in a cycle-bound graph, researchers have been trying to determine under what circumstances ``loopy probability propagation'' is effective for probabilistic inference. Despite several theoretical advances in our understanding of probability propagation in cycle-bound graphs, 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 probability propagation in a graph with a large number of cycles produces results that are far 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 probability propagation.
Joint work with Ralf Koetter, Nemanja Petrovic, Kannan Achan and Dave Munson
For related papers, see Brendan Frey's home page.
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