title: 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.
authors.forename: Juan G
authors.initials: JG
authors.lastname: Serra
authors.forename: Matteo
authors.initials: M
authors.lastname: Testa
authors.forename: Rafael
authors.initials: R
authors.lastname: Molina
authors.forename: Aggelos K
authors.initials: AK
authors.lastname: Katsaggelos