Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images

Authors:
Mingyuan Zhou;Haojun Chen;John Paisley;Lu Ren;Lingbo Li;Zhengming Xing;David Dunson;Guillermo Sapiro;Lawrence Carin
Affiliations:
Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA;Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA;Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA;Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA;Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA;Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA;Department of Statistics, Duke University, Durham, NC, USA;Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA;Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
Venue:
IEEE Transactions on Image Processing
Year:
2012

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Abstract

Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive, incomplete, and/or 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, uniformly selected at random. Spatial interrelationships 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.