Filtrage des échos ultrasonores en CND par la fonction de Cross Validation Généralisée (GCV)

Le Contrôle Non Destructif (CND) a pour objectif de répondre à plusieurs problèmes posés dans l'industrie à savoir : i) le problème de sensibilité liées à la détection de petits défauts noyés dans le bruit, ii) le problème de caractérisation qui concerne la classification des défauts détectés, iii) enfin le problème de résolution dans la séparation de défauts très rapprochés. Dans ce contexte, la détection des petits défauts noyés dans du bruit est le but principal des plus grands laboratoires de recherche en matière de CND. Dans ce travail nous introduisons l'opération de filtrage de bruit d'échos ultrasonores réels, provenant de pièces de différentes matières, dans le domaine temps-échelle. Le filtrage par seuillage est l'une des applications majeures de la transformée en Ondelettes (T.O) dans le domaine du traitement du signal. Les méthodes sous-jacentes remplacent les coefficients au-dessous d'un certain seuil par zéro et gardent ou rétrécissent le reste. Pour le choix du seuil, plusieurs méthodes existent. Nous présenterons ici, une méthode qui suppose le modèle de bruit blanc gaussien additif, cherchant un seuil qui minimise la fonction de cross validation généralisée (GCV), cette méthode présente l'avantage de ne pas avoir besoin de connaissance a priori sur la puissance du bruit qui affecte l'écho ultrasonore

Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators

We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric density model, we show that the resulting estimator is optimal in the minimax sense over all Besov balls under the $L^2$ risk, without any logarithm factor

Variational Multiscale Nonparametric Regression: Algorithms and Implementation

Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure.Comment: Codes are available at https://github.com/housenli/MIN

A nonlinear Stein based estimator for multichannel image denoising

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein's principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising technique

A wavelet thresholding method for vibration signals denoising of high-piled wharf structure based on a modified artificial bee colony algorithm

Vibration monitoring signals are widely used for damage alarming among the structural health monitoring system. However, these signals are easily corrupted by the environmental noise in the collecting that hampers the accuracy and reliability of measured results. In this paper, a modified artificial bee colony (MABC) algorithm-based wavelet thresholding method has been proposed for noise reduction in the real measured vibration signals. Kent chaotic map and general opposition-based learning strategies are firstly adopted to initialize the colony. Tournament selection mechanism is then employed to choose the food source. Finally, the Kent chaotic search is applied to exploit the global optimum solution according to the current optimal value. Moreover, a generalized cross validation (GCV) based fitness function is constructed without requiring foreknowledge of the noise-free signals. A physical model experiment for a high-piled wharf structure is implemented to verify the feasibility of the proposed signal denoising approach. Particle swarm optimization (PSO) algorithm, basic artificial bee colony (BABC) algorithm and Logistic chaos artificial bee colony (LABC) algorithm and are also taken as contrast tests. Comparison results demonstrate that the proposed algorithm outperforms the other algorithms in terms of convergence speed and precision, and can effectively reduce the noise from the measured vibration signals of the high-piled wharf structure

Machine Learning And Image Processing For Noise Removal And Robust Edge Detection In The Presence Of Mixed Noise

The central goal of this dissertation is to design and model a smoothing filter based on the random single and mixed noise distribution that would attenuate the effect of noise while preserving edge details. Only then could robust, integrated and resilient edge detection methods be deployed to overcome the ubiquitous presence of random noise in images. Random noise effects are modeled as those that could emanate from impulse noise, Gaussian noise and speckle noise. In the first step, evaluation of methods is performed based on an exhaustive review on the different types of denoising methods which focus on impulse noise, Gaussian noise and their related denoising filters. These include spatial filters (linear, non-linear and a combination of them), transform domain filters, neural network-based filters, numerical-based filters, fuzzy based filters, morphological filters, statistical filters, and supervised learning-based filters. In the second step, switching adaptive median and fixed weighted mean filter (SAMFWMF) which is a combination of linear and non-linear filters, is introduced in order to detect and remove impulse noise. Then, a robust edge detection method is applied which relies on an integrated process including non-maximum suppression, maximum sequence, thresholding and morphological operations. The results are obtained on MRI and natural images. In the third step, a combination of transform domain-based filter which is a combination of dual tree – complex wavelet transform (DT-CWT) and total variation, is introduced in order to detect and remove Gaussian noise as well as mixed Gaussian and Speckle noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on medical ultrasound and natural images. In the fourth step, a smoothing filter, which is a feed-forward convolutional network (CNN) is introduced to assume a deep architecture, and supported through a specific learning algorithm, l2 loss function minimization, a regularization method, and batch normalization all integrated in order to detect and remove impulse noise as well as mixed impulse and Gaussian noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on natural images for both specific and non-specific noise-level

Development of Some Novel Nonlinear and Adaptive Digital Image Filters for Efficient Noise Suppression

Some nonlinear and adaptive digital image filtering algorithms have been developed in this thesis to suppress additive white Gaussian noise (AWGN), bipolar fixed-valued impulse, also called salt and pepper noise (SPN), random-valued impulse noise (RVIN) and their combinations quite effectively. The present state-of-art technology offers high quality sensors, cameras, electronic circuitry: application specific integrated circuits (ASIC), system on chip (SOC), etc., and high quality communication channels. Therefore, the noise level in images has been reduced drastically. In literature, many efficient nonlinear image filters are found that perform well under high noise conditions. But their performance is not so good under low noise conditions as compared to the extremely high computational complexity involved therein. Thus, it is felt that there is sufficient scope to investigate and develop quite efficient but simple algorithms to suppress low-power noise in an image. When..