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. 1 Introduction Phase unwrapping is an easily stated, fundamental problem in image processing (Ghiglia and Pritt 1998).

The mystery of belief propagation (BP) decoder, especially of the turbo decoding, is studied from information geometrical viewpoint. The loopy belief network (BN) of turbo codes makes it difficult to obtain the true "belief" by BP, and the characteristics of the algorithm and its equilibrium are not clearly understood. Our study gives an intuitive understanding of the mechanism, and a new framework for the analysis. Based on the framework, we reveal basic properties of the turbo decoding.

Bayesian belief propagation in graphical models has been recently shown to have very close ties to inference methods based in statistical physics. After Yedidia et al. demonstrated that belief propagation fixed points correspond to extrema of the so-called Bethe free energy, Yuille derived a double loop algorithm that is guaranteed to converge to a local minimum of the Bethe free energy. Yuille's algorithm is based on a certain decomposition of the Bethe free energy and he mentions that other decompositions are possible and may even be fruitful. In the present work, we begin with the Bethe free energy and show that it has a principled interpretation as pairwise mutual information minimization and marginal entropy maximization (MIME). Next, we construct a family of free energy functions from a spectrum of decompositions of the original Bethe free energy. For each free energy in this family, we develop a new algorithm that is guaranteed to converge to a local minimum. Preliminary computer simulations are in agreement with this theoretical development.

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. 1 Introduction Phase unwrapping is an easily stated, fundamental problem in image processing (Ghiglia and Pritt 1998).

The mystery of belief propagation (BP) decoder, especially of the turbo decoding, is studied from information geometrical viewpoint. The loopy belief network (BN) of turbo codes makes it difficult to obtain the true "belief" by BP, and the characteristics of the algorithm and its equilibrium are not clearly understood. Our study gives an intuitive understanding of the mechanism, and a new framework for the analysis. Based on the framework, we reveal basic properties of the turbo decoding.

Bayesian belief propagation in graphical models has been recently shown to have very close ties to inference methods based in statistical physics. After Yedidia et al. demonstrated that belief propagation fixed points correspond to extrema of the so-called Bethe free energy, Yuille derived a double loop algorithm that is guaranteed to converge to a local minimum of the Bethe free energy. Yuille's algorithm is based on a certain decomposition of the Bethe free energy and he mentions that other decompositions are possible and may even be fruitful. In the present work, we begin with the Bethe free energy and show that it has a principled interpretation as pairwise mutual information minimization and marginal entropy maximization (MIME). Next, we construct a family of free energy functions from a spectrum of decompositions of the original Bethe free energy. For each free energy in this family, we develop a new algorithm that is guaranteed to converge to a local minimum. Preliminary computer simulations are in agreement with this theoretical development.

"fr in ge lin es" - boundaries across which wrappings have occurred .

The mystery of belief propagation (BP) decoder, especially of the turbo decoding, is studied from information geometrical viewpoint. The loopy belief network (BN) of turbo codes makes it difficult to obtain the true "belief" by BP, and the characteristics of the algorithm and its equilibrium arenot clearly understood. Our study gives an intuitive understanding of the mechanism, and a new framework for the analysis. Based on the framework, we reveal basic properties of the turbo decoding.

Yuille's algorithm is based on a certain decomposition of the Bethe

We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We then provide a knowledge compilation map, which analyzes a large number of existing target compilation languages according to their succinctness and their polytime transformations and queries. We argue that such analysis is necessary for placing new compilation approaches within the context of existing ones. We also go beyond classical, flat target compilation languages based on CNF and DNF, and consider a richer, nested class based on directed acyclic graphs (such as OBDDs), which we show to include a relatively large number of target compilation languages.