Mean Field Approximation for Fields of Experts

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概要

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• Fields of experts (FoE) model, which is regarded as a higher-order Markov random field whose clique potentials are modeled by the products of experts, matches spatial structures of natural images well, and therefore, it is an efficient prior of natural images. However, the FoE model does not readily admit efficient inferences because of the complexity of landscape of its energy function. In this paper, we propose an efficient mean field approximation for the FoE model by using a perturbative expansion in statistical mechanics. Our proposed mean field approximation can be applied to the FoE under general settings and can be solved in linear time with respect to the number of pixels. In the latter part of this paper, we apply our method to the image inpainting problem, and we show it gives results being the same or better than ones given by a simple gradient method proposed in the original work.

• 東北大学大学院情報科学研究科の論文

著者

• Yasuda Muneki

  Graduate School of Information Science, Tohoku University, Sendai 980-8579, Japan

• Tanaka Kazuyuki

  Graduate School of Information Science, Tohoku University, Sendai 980-8579, Japan

• YASUDA Muneki

  Graduate School of Science and Engineering, Yamagata University

関連論文

• Inverse Problem in Pairwise Markov Random Fields Using Loopy Belief Propagation
• Learning algorithm in restricted Boltzmann machines using Kullback-Leibler importance estimation procedure
• Bayesian Image Modeling by Means of a Generalized Sparse Prior and Loopy Belief Propagation
• Statistical Analysis of Gaussian Image Inpainting Problems
• Learning Algorithm for Boltzmann Machines Using Max-Product Algorithm and Pseudo-Likelihood
• Pseudo Temperature of Observed Data
• Learning Algorithm for Boltzmann Machines Using Max-Product Algorithm and Pseudo-Likelihood
• Mean Field Approximation for Fields of Experts
• Statistical Performance Analysis in Probabilistic Image Processing

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