Fast Dictionary Learning for Sparse Representations of Speech Signals

© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Published version: IEEE Journal of Selected Topics in Signal Processing 5(5): 1025-1031, Sep 2011. DOI: 10.1109/JSTSP.2011.2157892

Jitter-Adaptive Dictionary Learning - Application to Multi-Trial Neuroelectric Signals

Dictionary Learning has proven to be a powerful tool for many image processing tasks, where atoms are typically defined on small image patches. As a drawback, the dictionary only encodes basic structures. In addition, this approach treats patches of different locations in one single set, which means a loss of information when features are well-aligned across signals. This is the case, for instance, in multi-trial magneto- or electroencephalography (M/EEG). Learning the dictionary on the entire signals could make use of the alignement and reveal higher-level features. In this case, however, small missalignements or phase variations of features would not be compensated for. In this paper, we propose an extension to the common dictionary learning framework to overcome these limitations by allowing atoms to adapt their position across signals. The method is validated on simulated and real neuroelectric data.Comment: 9 pages, 5 figures, minor correction

Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques, and the fact that natural images are intrinsically sparse in some domain. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a pre-collected dataset of example image patches, and then for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image non-local self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page