Bayesian K-SVD Using Fast Variational Inference. Serra, J. G., Testa, M., Molina, R., & Katsaggelos, A. K. IEEE Transactions on Image Processing, 26(7):3344–3359, jul, 2017.
Bayesian K-SVD Using Fast Variational Inference [link]Paper  doi  abstract   bibtex   
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 fullyautomated 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.
@article{Juan2017a,
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 fullyautomated 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.},
author = {Serra, Juan G. and Testa, Matteo and Molina, Rafael and Katsaggelos, Aggelos K.},
doi = {10.1109/TIP.2017.2681436},
issn = {1057-7149},
journal = {IEEE Transactions on Image Processing},
keywords = {Bayesian modeling,Denoising,Dictionary learning,Inpainting,Sparse representation,Variational inference,k-SVD},
month = {jul},
number = {7},
pages = {3344--3359},
pmid = {28362587},
title = {{Bayesian K-SVD Using Fast Variational Inference}},
url = {http://ieeexplore.ieee.org/document/7875464/},
volume = {26},
year = {2017}
}

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