Effective SAR image despeckling based on bandlet and SRAD

Despeckling of a SAR image without losing features of the image is a daring task as it is intrinsically affected by multiplicative noise called speckle. This thesis proposes a novel technique to efficiently despeckle SAR images. Using an SRAD filter, a Bandlet transform based filter and a Guided filter, the speckle noise in SAR images is removed without losing the features in it. Here a SAR image input is given parallel to both SRAD and Bandlet transform based filters. The SRAD filter despeckles the SAR image and the despeckled output image is used as a reference image for the guided filter. In the Bandlet transform based despeckling scheme, the input SAR image is first decomposed using the bandlet transform. Then the coefficients obtained are thresholded using a soft thresholding rule. All coefficients other than the low-frequency ones are so adjusted. The generalized cross-validation (GCV) technique is employed here to find the most favorable threshold for each subband. The bandlet transform is able to extract edges and fine features in the image because it finds the direction where the function gives maximum value and in the same direction it builds extended orthogonal vectors. Simple soft thresholding using an optimum threshold despeckles the input SAR image. The guided filter with the help of a reference image removes the remaining speckle from the bandlet transform output. In terms of numerical and visual quality, the proposed filtering scheme surpasses the available despeckling schemes

Automatic intrapersonal variability modeling for offline signature augmentation

Orientador: Luiz Eduardo Soares de OliveiraCoorientadores: Robert Sabourin e Alceu de Souza Britto Jr..Tese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 19/07/2021Inclui referências: p. 93-102Área de concentração: Ciência da ComputaçãoResumo: Normalmente, em um cenario do mundo real, poucas assinaturas estao disponiveis para treinar um sistema de verificacao automatica de assinaturas (SVAA). Para resolver esse problema, diversas abordagens para a duplicacao de assinaturas estaticas foram propostas ao longo dos anos. Essas abordagens geram novas amostras de assinaturas sinteticas aplicando algumas transformacoes na imagem original da assinatura. Algumas delas geram amostras realistas, especialmente o duplicator. Este metodo utiliza um conjunto de parametros para modelar o comportamento do escritor (variabilidade do escritor) ao assinar. No entanto, esses parametros so empiricamente definidos. Este tipo de abordagem pode ser demorado e pode selecionar parametros que nao descrevem a real variabilidade do escritor. A principal hipotese desse trabalho e que a variabilidade do escritor observada no dominio da imagem tambem pode ser transferido para o dominio de caracteristicas. Portanto, este trabalho propoe um novo metodo para modelar automaticamente a variabilidade do escritor para a posterior duplicacao de assinaturas no dominio de imagem (duplicator) e dominio de caracteristicas (filtro Gaussiano e variacao do metodo de Knop). Este trabalho tambem propoe um novo metodo de duplicacao de assinaturas estaticas, que gera as amostras sinteticas diretamente no dominio de caracteristicas usando um filtro Gaussiano. Alem disso, uma nova abordagem para avaliar a qualidade de amostras sinteticas no dominio de caracteristicas e apresentada. As limitacoes e vantagens de ambas as abordagens de duplicacao de assinaturas tambem sao exploradas. Alem de usar a nova abordagem para avaliar a qualidade das amostras, o desempenho de um SVAA e avaliado usando as amostras e tres bases de assinaturas estaticas bem conhecidas: a GPDS-300, a MCYT-75 e a CEDAR. Para a mais utilizada, GPDS-300, quando o classificador SVM foi treinando com somente uma assinatura genuina por escritor, ele obteve um Equal Error Rate (EER) de 5,71%. Quando o classificador tambem utilizou as amostras sinteticas geradas no dominio de imagem, o EER caiu para 1,08%. Quando o classificador foi treinado com as amostras geradas pelo filtro Gaussiano, o EER caiu para 1,04%.Abstract: Normally, in a real-world scenario, there are few signatures available to train an automatic signature verification system (ASVS). To address this issue, several offline signature duplication approaches have been proposed along the years. These approaches generate a new synthetic signature sample applying some transformations in the original signature image. Some of them generate realistic samples, specially the duplicator. This method uses a set of parameters to model the writer's behavior (writer variability) during the signing act. However, these parameters are empirically defined. This kind of approach can be time consuming and can select parameters that do not describe the real writer variability. The main hypothesis of this work is that the writer variability observed in the image space can be transferred to the feature space as well. Therefore, this work proposes a new method to automatically model the writer variability for further signature duplication in the image (duplicator) and the feature space (Gaussian filter and a variation of Knop's method). This work also proposes a new offline signature duplication method, which directly generates the synthetic samples in the feature space using a Gaussian filter. Furthermore, a new approach to assess the quality of the synthetic samples in the feature space is introduced. The limitations and advantages of both signature augmentation approaches are also explored. Despite using the new approach to assess the quality of the samples, the performance of an ASVS was assessed using them and three well-known offline signature datasets: GPDS-300, MCYT-75, and CEDAR. For the most used one, GPDS-300, when the SVM classifier was trained with only one genuine signature per writer, it achieved an Equal Error Rate (EER) of 5.71%. When the classifier also was trained with the synthetic samples generated in the image space, the EER dropped to 1.08%. When the classifier was trained using the synthetic samples generated by the Gaussian filter, the EER dropped to 1.04%

Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging variance, which hinders the use of conventional convergence analysis techniques that rely on the existence of the second-order moments. In this paper, we provide convergence guarantees for SGD under a state-dependent and heavy-tailed noise with a potentially infinite variance, for a class of strongly convex objectives. In the case where the $p$-th moment of the noise exists for some $p\in [1,2)$, we first identify a condition on the Hessian, coined '$p$-positive (semi-)definiteness', that leads to an interesting interpolation between positive semi-definite matrices ($p=2$) and diagonally dominant matrices with non-negative diagonal entries ($p=1$). Under this condition, we then provide a convergence rate for the distance to the global optimum in $L^p$. Furthermore, we provide a generalized central limit theorem, which shows that the properly scaled Polyak-Ruppert averaging converges weakly to a multivariate $\alpha$-stable random vector. Our results indicate that even under heavy-tailed noise with infinite variance, SGD can converge to the global optimum without necessitating any modification neither to the loss function or to the algorithm itself, as typically required in robust statistics. We demonstrate the implications of our results to applications such as linear regression and generalized linear models subject to heavy-tailed data

Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections

Gaussian noise injections (GNIs) are a family of simple and widely-used regularisation methods for training neural networks, where one injects additive or multiplicative Gaussian noise to the network activations at every iteration of the optimisation algorithm, which is typically chosen as stochastic gradient descent (SGD). In this paper we focus on the so-called `implicit effect' of GNIs, which is the effect of the injected noise on the dynamics of SGD. We show that this effect induces an asymmetric heavy-tailed noise on SGD gradient updates. In order to model this modified dynamics, we first develop a Langevin-like stochastic differential equation that is driven by a general family of asymmetric heavy-tailed noise. Using this model we then formally prove that GNIs induce an `implicit bias', which varies depending on the heaviness of the tails and the level of asymmetry. Our empirical results confirm that different types of neural networks trained with GNIs are well-modelled by the proposed dynamics and that the implicit effect of these injections induces a bias that degrades the performance of networks.Comment: Main paper of 12 pages, followed by appendi

Wavelet-based noise reduction of cDNA microarray images

The advent of microarray imaging technology has lead to enormous progress in the life sciences by allowing scientists to analyze the expression of thousands of genes at a time. For complementary DNA (cDNA) microarray experiments, the raw data are a pair of red and green channel images corresponding to the treatment and control samples. These images are contaminated by a high level of noise due to the numerous noise sources affecting the image formation. A major challenge of microarray image analysis is the extraction of accurate gene expression measurements from the noisy microarray images. A crucial step in this process is denoising, which consists of reducing the noise in the observed microarray images while preserving the signal information as much as possible. This thesis deals with the problem of developing novel methods for reducing noise in cDNA microarray images for accurate estimation of the gene expression levels. Denoising methods based on the wavelet transform have shown significant success when applied to natural images. However, these methods are not very efficient for reducing noise in cDNA microarray images. An important reason for this is that existing methods are only capable of processing the red and green channel images separately. In doing so. they ignore the signal correlation as well as the noise correlation that exists between the wavelet coefficients of the two channels. The primary objective of this research is to design efficient wavelet-based noise reduction algorithms for cDNA microarray images that take into account these inter-channel dependencies by 'jointly' estimating the noise-free coefficients in both the channels. Denoising algorithms are developed using two types of wavelet transforms, namely, the frequently-used discrete wavelet transform (DWT) and the complex wavelet transform (CWT). The main advantage of using the DWT for denoising is that this transform is computationally very efficient. In order to obtain a better denoising performance for microarray images, however, the CWT is preferred to DWT because the former has good directional selectivity properties that are necessary for better representation of the circular edges of spots. The linear minimum mean squared error and maximum a posteriori estimation techniques are used to develop bivariate estimators for the noise-free coefficients of the two images. These estimators are derived by utilizing appropriate joint probability density functions for the image coefficients as well as the noise coefficients of the two channels. Extensive experimentations are carried out on a large set of cDNA microarray images to evaluate the performance of the proposed denoising methods as compared to the existing ones. Comparisons are made using standard metrics such as the peak signal-to-noise ratio (PSNR) for measuring the amount of noise removed from the pixels of the images, and the mean absolute error for measuring the accuracy of the estimated log-intensity ratios obtained from the denoised version of the images. Results indicate that the proposed denoising methods that are developed specifically for the microarray images do, indeed, lead to more accurate estimation of gene expression levels. Thus, it is expected that the proposed methods will play a significant role in improving the reliability of the results obtained from practical microarray experiments

Modélisation stochastique pour l'analyse d'images texturées (approches Bayésiennes pour la caractérisation dans le domaine des transformées)

Le travail présenté dans cette thèse s inscrit dans le cadre de la modélisation d images texturées à l aide des représentations multi-échelles et multi-orientations. Partant des résultats d études en neurosciences assimilant le mécanisme de la perception humaine à un schéma sélectif spatio-fréquentiel, nous proposons de caractériser les images texturées par des modèles probabilistes associés aux coefficients des sous-bandes. Nos contributions dans ce contexte concernent dans un premier temps la proposition de différents modèles probabilistes permettant de prendre en compte le caractère leptokurtique ainsi que l éventuelle asymétrie des distributions marginales associées à un contenu texturée. Premièrement, afin de modéliser analytiquement les statistiques marginales des sous-bandes, nous introduisons le modèle Gaussien généralisé asymétrique. Deuxièmement, nous proposons deux familles de modèles multivariés afin de prendre en compte les dépendances entre coefficients des sous-bandes. La première famille regroupe les processus à invariance sphérique pour laquelle nous montrons qu il est pertinent d associer une distribution caractéristique de type Weibull. Concernant la seconde famille, il s agit des lois multivariées à copules. Après détermination de la copule caractérisant la structure de la dépendance adaptée à la texture, nous proposons une extension multivariée de la distribution Gaussienne généralisée asymétrique à l aide de la copule Gaussienne. L ensemble des modèles proposés est comparé quantitativement en terme de qualité d ajustement à l aide de tests statistiques d adéquation dans un cadre univarié et multivarié. Enfin, une dernière partie de notre étude concerne la validation expérimentale des performances de nos modèles à travers une application de recherche d images par le contenu textural. Pour ce faire, nous dérivons des expressions analytiques de métriques probabilistes mesurant la similarité entre les modèles introduits, ce qui constitue selon nous une troisième contribution de ce travail. Finalement, une étude comparative est menée visant à confronter les modèles probabilistes proposés à ceux de l état de l art.In this thesis we study the statistical modeling of textured images using multi-scale and multi-orientation representations. Based on the results of studies in neuroscience assimilating the human perception mechanism to a selective spatial frequency scheme, we propose to characterize textures by probabilistic models of subband coefficients.Our contributions in this context consist firstly in the proposition of probabilistic models taking into account the leptokurtic nature and the asymmetry of the marginal distributions associated with a textured content. First, to model analytically the marginal statistics of subbands, we introduce the asymmetric generalized Gaussian model. Second, we propose two families of multivariate models to take into account the dependencies between subbands coefficients. The first family includes the spherically invariant processes that we characterize using Weibull distribution. The second family is this of copula based multivariate models. After determination of the copula characterizing the dependence structure adapted to the texture, we propose a multivariate extension of the asymmetric generalized Gaussian distribution using Gaussian copula. All proposed models are compared quantitatively using both univariate and multivariate statistical goodness of fit tests. Finally, the last part of our study concerns the experimental validation of the performance of proposed models through texture based image retrieval. To do this, we derive closed-form metrics measuring the similarity between probabilistic models introduced, which we believe is the third contribution of this work. A comparative study is conducted to compare the proposed probabilistic models to those of the state-of-the-art.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Deep Learning in Medical Image Analysis

The accelerating power of deep learning in diagnosing diseases will empower physicians and speed up decision making in clinical environments. Applications of modern medical instruments and digitalization of medical care have generated enormous amounts of medical images in recent years. In this big data arena, new deep learning methods and computational models for efficient data processing, analysis, and modeling of the generated data are crucially important for clinical applications and understanding the underlying biological process. This book presents and highlights novel algorithms, architectures, techniques, and applications of deep learning for medical image analysis

A precise bare simulation approach to the minimization of some distances. Foundations

In information theory -- as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -- many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous examples. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface)