The problem of learning a data-adaptive dictionary for a very large collection of signals is addressed. This paper proposes a statistical model and associated variational Bayesian (VB) inference for simultaneously learning the dictionary and performing sparse coding of the signals. The model builds upon beta process factor analysis (BPFA), with the number of factors automatically inferred, and posterior distributions are estimated for both the dictionary and the signals. Crucially, an online learning procedure is employed, allowing scalability to very large datasets which would be beyond the capabilities of existing batch methods. State-of-the-art performance is demonstrated by experiments with large natural images containing tens of millions of pixels.

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.

A new Bayesian model is proposed, integrating dictionary learning and topic modeling into a unified framework. The model is applied to cluster multiple images, and a subset of the images may be annotated. Example results are presented on the MNIST digit data and on the Microsoft MSRC multi-scene image data. These results reveal the working mechanisms of the model and demonstrate state-of-the-art performance.