## 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.

Original language | English (US) |
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Article number | 7875464 |

Pages (from-to) | 3344-3359 |

Number of pages | 16 |

Journal | IEEE Transactions on Image Processing |

Volume | 26 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2017 |

## Keywords

- Bayesian modeling
- Denoising
- Dictionary learning
- Inpainting
- Sparse representation
- Variational inference
- k-SVD

## ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design