Nonparametric Bayesian dictionary learning for sparse image representations

Abstract—Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive, incomplete, and/or noisy measurements. A truncated beta-Bernoulli process is em-ployed 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. Index Terms—Bayesian nonparametrics, compressive sensing, dictionary learning, factor analysis, image denoising, image inter-polation, sparse coding