title: Nonparametric Bayesian dictionary learning for analysis of noisy and incomplete images.
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.
authors.affiliation: Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708-0291, USA.
authors.forename: Mingyuan
authors.initials: M
authors.lastname: Zhou
authors.forename: Haojun
authors.initials: H
authors.lastname: Chen
authors.forename: John
authors.initials: J
authors.lastname: Paisley
authors.forename: Lu
authors.initials: L
authors.lastname: Ren
authors.forename: Lingbo
authors.initials: L
authors.lastname: Li
authors.forename: Zhengming
authors.initials: Z
authors.lastname: Xing
authors.forename: David
authors.initials: D
authors.lastname: Dunson
authors.forename: Guillermo
authors.initials: G
authors.lastname: Sapiro
authors.forename: Lawrence
authors.initials: L
authors.lastname: Carin
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001499:Bayes Theorem; D003627:Data Interpretation, Statistical; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity