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Non-parametric Bayesian techniques are considered for learningdictionaries for sparse image representations, with applications indenoising, inpainting and compressive sensing. The four maincontributions of our paper are:
The dictionary is learned using a beta process construction, andtherefore the number of dictionary elements and their relativeimportance may be inferred non-parametrically.For the denoising and inpainting applications, we do not have toassume a priori knowledge of the noise variance or sparsity level.The spatial inter-relationships between different components inimages are exploited by use of the Dirichlet process and a probitstick-breaking process.Using learned dictionaries, inferred off-line or in situ, theproposed approach yields CS performance that is markedly betterthan existing standard CS methods as applied to imagery.
Non-Parametric Bayesian Dictionary Learning for Sparse Image RepresentationsMingyuan Zhou, Haojun Chen, John Paisley, Lu Ren, 1Guillermo Sapiro and Lawrence Carin
Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA1Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA
{mz1, hc44, jwp4, lr, lcarin}@ee.duke.edu, {guille}@umn.edu
Introduction
Model and Inference
Full likelihood of the Model
Gibbs Sampling Inference
Image denoising
Image inpainting
Applications
Compressive sensing
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