Bayesian K-SVD Using Fast Variational Inference

Abstract

Recent work in signal processing in general and image processing in particular deals with sparse representation related problems. Two such problems are of paramount importance: an overriding need for designing a well-suited overcomplete dictionary containing a redundant set of atoms—i.e., basis signals—and how to find a sparse representation of a given signal with respect to the chosen dictionary. Dictionary learning techniques, among which we find the popular K-singular value decomposition algorithm, tackle these problems by adapting a dictionary to a set of training data. A common drawback of such techniques is the need for parameter-tuning. In order to overcome this limitation, we propose a fully-automated Bayesian method that considers the uncertainty of the estimates and produces a sparse representation of the data without prior information on the number of non-zeros in each representation vector. We follow a Bayesian approach that uses a three-tiered hierarchical prior to enforce sparsity on the representations and develop an efficient variational inference framework that reduces computational complexity. Furthermore, we describe a greedy approach that speeds up the whole process. Finally, we present experimental results that show superior performance on two different applications with real images: denoising and inpainting.