Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images
IMA preprint series no. 2307
MINNESOTA UNIV MINNEAPOLIS INST FOR MATHEMATICS AND ITS APPLICATIONS
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Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive incomplete andor noisy measurements. A truncated beta-Bernoulli process is employed to infer an appropriate dictionary for the data under test, and also for image recovery. In the context of compressive sensing, significant improvements in image recovery are manifested using learned dictionaries, relative to using standard orthonormal image expansions. The compressive-measurement projections are also optimized for the learned dictionary. Additionally, we consider simpler incomplete measurements defined by measuring a subset of image pixels, selected uniformly at random connections are made to matrix completion and union-of-subspace models, providing a link between matrix completion and image processing. Spatial inter-relationships within imagery are exploited through use of the Dirichlet and probit stick-breaking processes. Several example results are presented, with comparisons to other methods in the literature.
- Statistics and Probability