Morphological Diversity and Sparse Image Denoising

International audienceOvercomplete representations are attracting interest in image processing theory, particularly due to their potential to generate sparse representations of data based on their morphological diversity. We here consider a scenario of image denoising using an overcomplete dictionary of sparse linear transforms. Rather than using the basic approach where the denoised image is obtained by simple averaging of denoised estimates provided by each sparse transform, we here develop an elegant bayesian framework to optimally combine the individual estimates. Our derivation of the optimally combined denoiser relies on a scale mixture of gaussian (SMG) prior on the coefficients in each representation transform. Exploiting this prior, we design a bayesian 2-risk (mean field) nonlinear estimator and we derive a closed-form for its expression when the SMG specializes to the Bessel K form prior. Experimental results are carried out to show the striking profits gained from exploiting sparsity of data and their morphological diversity

Multispectral palmprint recognition using Pascal coefficients-based LBP and PHOG descriptors with random sampling

Local binary pattern (LBP) algorithm and its variants have been used extensively to analyse the local textural features of digital images with great success. Numerous extensions of LBP descriptors have been suggested, focusing on improving their robustness to noise and changes in image conditions. In our research, inspired by the concepts of LBP feature descriptors and a random sampling subspace, we propose an ensemble learning framework, using a variant of LBP constructed from Pascal’s coefficients of n-order and referred to as a multiscale local binary pattern. To address the inherent overfitting problem of linear discriminant analysis, PCA was applied to the training samples. Random sampling was used to generate multiple feature subsets. In addition, in this work, we propose a new feature extraction technique that combines the pyramid histogram of oriented gradients and LBP, where the features are concatenated for use in the classification. Its performance in recognition was evaluated using the Hong Kong Polytechnic University database. Extensive experiments unmistakably show the superiority of the proposed approach compared to state-of-the-art techniques

Multi-spectral palmprint recognition based on oriented multiscale log-Gabor filters

Among several palmprint recognition methods proposed recently, coding-based approaches using multi-spectral palmprint images are attractive owing to their high recognition rates. Aiming to further improve the performance of these approaches, this paper presents a novel multi-spectral palmprint recognition approach based on oriented multiscale log-Gabor filters. The proposed method aims to enhance the recognition performances by proposing novel solutions at three stages of the recognition process. Inspired by the bitwise competitive coding, the feature extraction employs a multi-resolution log-Gabor filtering where the final feature map is composed of the winning codes of the lowest filters’ bank response. The matching process employs a bitwise Hamming distance and Kullback–Leibler divergence as novel metrics to enable an efficient capture of the intra- and inter-similarities between palmprint feature maps. Finally, the decision stage is carried pout using a fusion of the scores generated from different spectral bands to reduce overlapping. In addition, a fusion of the feature maps through two proposed novel feature fusion techniques to allow us to eliminate the inherent redundancy of the features of neighboring spectral bands is also proposed. The experimental results obtained using the multi-spectral palmprint database MS-PolyU have shown that the proposed method achieves high accuracy in mono-spectral and multi-spectral recognition performances for both verification and identification modes; and also outperforms the state-of-the-art methods

Multivariate statistical modelization of images in the oriented and non-oriented multiscale transforms domain

Dans cet article, nous proposons un modèle statistique multivarié, à savoir le modèle Formes K de Bessel Multivarié (MBKF), pour caractériser les dépendances inter- et intra-échelle des coefficients d'images dans le domaine des transformées multi-échelles parcimonieuses orientées et non-orientées. Notre modèle est basé sur une extension multivariée de la distribution des Formes K de Bessel. Pour mettre en application ce modèle, nous avons proposé une forme analytique pour sa classe de PDFs, ainsi que des estimateurs pour estimer ses hyperparamètres. Ensuite, nous l'avons comparé avec d'autres modèles multivariés proposés dans la littérature

Approches bayésiennes pour le débruitage des images dans le domaine des transformées multi-échelles parcimonieuses orientées et non orientées

Image data observed at the output of an image acquisition device are generally degraded by the sensor noise. The task which aims at recovering a good quality image from its noisy observations is widely known as denoising. Denoising has been at the heart of a flurry of research activity in the image processing literature. In this work, after defining the denoising problem when data are corrupted by an additive gaussian noise, we provide an extensive and methodical review of the literature. Most of image denoising methods try to narrow down the class of candidate solutions by imposing some prior regularity constraints on the recovered solution. We have chosen to formulate our prior in a bayesian framework, through multi-scale transform coefficients of the image. Towards this end, and by appropriately exploiting the sparsity of these multi-scale representations, we designed prior models to capture the marginal and joint statistics of such coefficients in oriented (e.g. curvelets) and non-oriented (e.g. wavelets) multiscale pyramids. These priors were then utilized in newly proposed bayesian denoisers. The implementation of these bayesian estimators relies on two key steps for which we suggested efficient solutions: (i) estimate the hyperparameters of the prior model in presence of noise, and (ii) find an analytical form for the corresponding bayesian estimator. In the first part of this thesis, we designed term-by-term univariate bayesian estimators by taking advantage of the marginal statistics of coefficients of images in sparse multiscale representations, e.g. wavelets. These marginal statistics were modelled analytically using alpha-stable and Bessel K Form distributions. In the second part, we improved upon the performance of univariate estimators by introducing the geometrical information contained in the neighborhood of each representation coefficients. More precisely, we proposed a multivariate statistical bayesian framework which takes into account the intra- and inter-scale dependencies of coefficients and models the joint statistics of groups of coefficients in the curvelet and the undecimated wavelet domains. The associated multivariate bayesian estimator was also provided based on a multivariate extension of the Bessel K Form distribution. A comprehensive comparative study has been carried out to compare our denoising algorithms to state-of-the-art competitors.Les images issues d'une chaîne d'acquisition sont généralement dégradées par le bruit du capteur. La tâche qui consiste à restaurer une image de bonne qualité à partir de sa version bruitée est communément appelée débruitage. Celui-ci a engendré une importante littérature en pré-traitement des images. Lors de ce travail de thèse, et après avoir posé le problème du débruitage en présence d'un bruit additif gaussien, nous avons effectué un état de l'art méthodique sur ce sujet. Les méthodes présentées cherchent pour la plupart à reconstruire une solution qui présente une certaine régularité. En s'appuyant sur un cadre bayésien, la régularité de la solution, qui peut être imposée de différentes manières, a été formellement mise en place en passant dans le domaine des transformées multi-échelle. Ainsi, afin d'établir un modèle d'a priori, nous avons mené une modélisation des statistiques marginales et jointes des coefficients d'images dans le domaine des transformées multi-échelles orientées (e.g. curvelets) et non-orientées (e.g. ondelettes). Ensuite, nous avons proposé de nouveaux estimateurs bayésiens pour le débruitage. La mise en œuvre de ces estimateurs est effectuée en deux étapes, la première consistant à estimer les hyperparamètres du modèle de l'a priori en présence du bruit et la seconde à trouver une forme analytique pour l'estimateur bayésien correspondant. Dans un premier temps, nous avons mis en place des estimateurs bayésiens univariés en mettant à profit les statistiques marginales des coefficients des images dans des représentations multi-échelle comme les ondelettes. Ces lois marginales ont été analytiquement modélisées par le biais des distributions: ?-stable et les Formes K de Bessel. Dans un second temps, nous avons amélioré les performances de nos estimateurs univariés en introduisant l'information géométrique dans le voisinage des coefficients. Plus précisément, nous avons proposé un cadre statistique bayésien multivarié permettant de prendre en compte les dépendances inter- et intra-échelle des coefficients, en mettant à profit les statistiques jointes de ces derniers dans le domaine des curvelets et des ondelettes non décimées. Ensuite, nous avons mis en place l'estimateur bayésien multivarié correspondant basé sur une extension multivariée de la distribution des Formes K de Bessel. Une large étude comparative a finalement été menée afin de confronter nos algorithmes de débruitage à d'autres débruiteurs de l'état de l'art

Algorithme EM pour l'estimation des hyperparamètres du débruiteur bayésien d'images basé sur l'a priori des formes K de Bessel

International audienceNous présentons un nouvel estimateur des hyperparamètres associés au débruiteur bayésien d'images que nous avons récemment développé, utilisant comme a priori une nouvelle classe de distributions, les Formes K de Bessel. Plus exactement, cette approche est basée sur l'algorithme EM. Les simulations menées montrent que cet estimateur offre des performances bonnes et qui dépasse légèrement l'estimateur des hyperparamètres avec la méthode des cumulants proposée dans [1]. Des résultats expérimentaux sont montrés pour illustrer les performances de notre débruiteur bayésien comparé à d'autres débruiteurs développés dans des contextes classique et bayésien

Recent Advances in Biometrics and Its Applications

Biometric recognition has become a burgeoning research area due to the industrial and government needs for security and privacy concerns [...

Wavelet Denoising Based on the MAP Estimation Using the BKF Prior With Application to Images and EEG Signals

This paper presents a novel nonparametric Bayesian estimator for signal and image denoising in the wavelet domain. This approach uses a prior model of the wavelet coefficients designed to capture the sparseness of the wavelet expansion. A new family of Bessel K Form (BKF) densities are designed to fit the observed histograms, so as to provide a probabilistic model for the marginal densities of the wavelet coefficients. This paper first shows how the BKF prior can characterize images belonging to Besov spaces. Then, a new hyper-parameters estimator based on EM algorithm is designed to estimate the parameters of the BKF density; and, it is compared with a cumulants-based estimator. Exploiting this prior model, another novel contribution is to design a Bayesian denoiser based on the Maximum A Posteriori (MAP) estimation under the 0–1 loss function, for which we formally establish the mathematical properties and derive a closed-form expression. Finally, a comparative study on a digitized database of natural images and biomedical signals shows the effectiveness of this new Bayesian denoiser compared to other classical and Bayesian denoising approaches. Results on biomedical data illustrate the method in the temporal as well as the time-frequency domain

Unsupervised white matter fiber tracts clustering methodology with application on brain MRI data

Understanding the geometrical organization of the white matter fibers is one of the current challenges in neuroimaging. White matter fiber clustering technique appears to a corner stone to solve this problem. In this paper, we propose a rapid and efficient unsupervised white matter fiber tracts clustering methodology based on a novel fiber tract similarity metric and an approximation of the k-means algorithm. In this approach, we first define a distance metric capable to quantify the intrinsic geometry of the fiber tracts. This metric is based on a combination of the symmetric Chamfer distance and mean local orientation measures between fiber tracts. Second, we perform the randomized feature selection algorithm proposed for the k-means problem to reduce the dimensionality of the distance data matrix generated from all the fiber tracts using the defined metric. The k-means algorithm is then performed on the reduced distance matrix to cluster the fiber tracts. Finally, we evaluate the method on the synthetic data and in vivo adult brain dataset