Darbe analizuojama diskrečioji Le Gall transformacija (DLGT) yra viena iš bangelių transformacijų, kurios naudojamos skaitmeninių vaizdų glaudinime. Vaizdų glaudinimas ypač svarbus, kai kalbama apie vaizdų siuntimą mažo pralaidumo kompiuteriniu kanalu. Šiai problemai spręsti pasitelkiama diskrečioji Le Gall transformacija, bei didelis dėmesys darbe skirtas vaizdo fragmento DLGT spektrui. Šio spektro radimui sukurtas ir realizuotas naujas algoritmas − greitoji procedūra. Palyginamosios analizės metu įrodyta, kad sukurta greitoji procedūra randa vaizdo fragmento DLGT spektrą daugiau nei 50 kartų greičiau nei tiesiogiai taikant DLGT vaizdo fragmentui. Darbo pradžioje aptariamos pagrindinės bangelių ir jų transformacijų savybės. Šių savybių svarba iliustruojama pateiktais pavyzdžiais ir sąsajomis su taikymu praktikoje. Viena iš svarbesnių aptariamų savybių būtų transformacijos lokalizavimas erdvėje. Nors DLGT pilnai netenkina šios savybės, tačiau darbe apžvelgtas dekoreliacijos metodas leidžia išspręsti šią problemą. Be to, pateikiami išsamūs DLGT algoritmai vienmačiams ir dvimačiams vaizdams. Šių algoritmų dėka buvo sukurta programinė įranga, padedanti analizuoti DLGT. Galiausiai darbo pabaigoje pateikiama sukurtos programinės įrangos instrukcija. / In this paper the main attention is dedicated to discrete Le Gall transformation (DLGT), the family of discrete wavelets transformations, which usage in the image compression is quite popular. Image compression is very important when it comes to low bandwidth network and computer channels. To deal with this problem the discrete Le Gall wavelets are brought up and focused on the image fragment DLGT spectrum. For calculation of this spectrum the new fast procedure is suggested and realized. In comparative analysis the fast procedure is proved to work more than 50 times faster than applying DLGT direct to image fragment. In the beginning of this paper the main concepts of wavelets and their transformations are analyzed. An importance of these properties is illustrated by examples and applications in practice. One of the most important properties is localization in space. Even though DLGT does not fully meet this property decorrelation technique, introduced in paper, benefits in solving localization problem. Moreover, DLGT algorithms are proposed for one-dimensional and 2-dimensional images. According to these algorithms the new program was created, which is dedicated for image analysis. Finally, in the end of paper the instructions of program are presented.

LISA Pathfinder (LPF) has been a space mission led by ESA with NASA contributions, operating between March 2016 and July 2017. LPF demonstrated the feasibility of setting bodies in space along freely-falling geodetic trajectories, complying with the residual acceleration requirements of the future gravitational-wave observatory LISA. After operations, the LPF Collaboration pointed out that two phenomena, affecting the sub-mHz performance, were not completely understood and needed deeper analyses. This, despite performing better than requirements. Such phenomena are, namely, the low-frequency acceleration noise, and the sub-pN transient acceleration glitches. This thesis work focuses entirely on analyzing these observations, in view of the future mission LISA. Regarding the low-frequency sub-mHz noise, first, we make a preliminary analysis. We investigate its evolution in time, its properties, its stability, and its nature. We find that the low-frequency noise has had a remarkably stable behavior for nearly two years, but noise fluctuations are not compatible with an overall unique noise. We develop results on multivariate spectral estimation. Implementing results from complex-variable statistics, we show that cross-power spectral density matrices follow complex-Wishart probability distributions; we develop a Bayesian tool for the posterior inference of spectral parameters. We develop decorrelation tools to understand the measured noise's physical origin. In particular, we aim at finding, if any, correlations between the main acceleration measurement and synchronously measured time series. Then, we summarize the most recent understanding of the LPF acceleration performance. We expand previous analyses about the LPF outgassing environment, through the analysis of the white "Brownian" noise, and the long-term quasi-static acceleration drift observed on LPF, proposing a physical model. We extensively analyze the second phenomenon impacting low-frequency performances, the acceleration transient glitches. We show that LPF glitches spanned a wide range of amplitudes, transferring impulses between a few fN s, to some nN s, and showing durations ranging from a few seconds to hours. We show that LPF glitches fall into two rather distinct categories: fast transients in the interferometric motion readout and long-lasting sub-pN force transient events, acting on the test masses. We present an analysis of the physical and statistical properties of both, including a cross-investigation with other time series and other dynamical variables, and examine the possible sources of glitches, identifying the most likely ones.

Existe uma variedade de modelos de dispersão de poluentes, em geral, os modelos gaussianos são usados em todo o mundo por agências ambientais com intuito de regulação. O modelo CALPUFF é um deles. Neste estudo, _e avaliada a influência de escalas de tempo de descorrelação no sistema de modelagem CALPUFF, sob condições atmosféricas neutras. Para fazer isso uma nova parametrização das escalas de tempo descorrelação é proposta. Uma distribuição espectral de um perfil de velocidade euleriana e uma for- mutação da evolução das escalas temporais de descorrelação Lagrangiana são utilizadas como os mecanismos forçantes na dispersão turbulenta, numa camada limite dominada pelo cisalhamento do vento. O desempenho do modelo foi estabelecido com a comparação das concentrações superficiais do experimento Over-Land Alongwind Dispersion. Emissões de fontes em linha foram avaliadas com o modelo CALPUFF com distintas formas de inicialização. Um segundo modelo também foi testado, normalmente utilizado para estudar e prever o impacto ambiental e validar parametrizações turbulentas. É o modelo estocástico de partículas Lagrangiano LAMBDA. Também neste estudo, os resultados do modelo LAMBDA e CALPUFF enfatizam a capacidade da nova derivação de escalas de tempo em representar o comportamento estocástico desconhecido do fenômeno da dispersão de poluentes. / There exists a variety of pollution of dispersion models and in general, Gaussian models are used worldwide by environmental agencies in regulatory applications. The CALPUFF model is one of them. In this study, the in uence of decorrelation time scales in the CALPUFF modeling system under neutral conditions is evaluated. To do this a new parameterization of decorrelation time scales is proposed. A spectral distribution of an Eulerian velocity pro le and a formulation of the evolution of the Lagrangian decorrela- tion timescales are used as the forcing mechanisms (shear-dominated boundary layer) for the turbulent dispersion. The model performance was established by comparing ground- level concentrations with Over-Land Alongwind Dispersion experimental results. Line source emissions was evaluated using the CALPUFF model with different forms of the initialization. A second model was also tested, normally used to study and predict the environmental impact and validate turbulent parameterizations. Is the stochastic La- grangian dispersion model LAMBDA (Ferrero and Anfossi, 1998). Also in this study the model LAMBDA and CALPUFF results emphasized the ability of the new derivation of decorrelation time scales to represent the unknown stochastic behavior.

We live in a dynamic world full of noises and interferences. The conventional acoustic echo cancellation (AEC) framework based on the least mean square (LMS) algorithm by itself lacks the ability to handle many secondary signals that interfere with the adaptive filtering process, e.g., local speech and background noise. In this dissertation, we build a foundation for what we refer to as the system approach to signal enhancement as we focus on the AEC problem. We first propose the residual echo enhancement (REE) technique that utilizes the error recovery nonlinearity (ERN) to "enhances" the filter estimation error prior to the filter adaptation. The single-channel AEC problem can be viewed as a special case of semi-blind source separation (SBSS) where one of the source signals is partially known, i.e., the far-end microphone signal that generates the near-end acoustic echo. SBSS optimized via independent component analysis (ICA) leads to the system combination of the LMS algorithm with the ERN that allows for continuous and stable adaptation even during double talk. Second, we extend the system perspective to the decorrelation problem for AEC, where we show that the REE procedure can be applied effectively in a multi-channel AEC (MCAEC) setting to indirectly assist the recovery of lost AEC performance due to inter-channel correlation, known generally as the "non-uniqueness" problem. We develop a novel, computationally efficient technique of frequency-domain resampling (FDR) that effectively alleviates the non-uniqueness problem directly while introducing minimal distortion to signal quality and statistics. We also apply the system approach to the multi-delay filter (MDF) that suffers from the inter-block correlation problem. Finally, we generalize the MCAEC problem in the SBSS framework and discuss many issues related to the implementation of an SBSS system. We propose a constrained batch-online implementation of SBSS that stabilizes the convergence behavior even in the worst case scenario of a single far-end talker along with the non-uniqueness condition on the far-end mixing system. The proposed techniques are developed from a pragmatic standpoint, motivated by real-world problems in acoustic and audio signal processing. Generalization of the orthogonality principle to the system level of an AEC problem allows us to relate AEC to source separation that seeks to maximize the independence, hence implicitly the orthogonality, not only between the error signal and the far-end signal, but rather, among all signals involved. The system approach, for which the REE paradigm is just one realization, enables the encompassing of many traditional signal enhancement techniques in analytically consistent yet practically effective manner for solving the enhancement problem in a very noisy and disruptive acoustic mixing environment.

A white Gaussian noise measurement model is widely used in target tracking problem formulation. In practice, the measurement noise may not be white. This phenomenon is due to the scintillation of the target. In many radar systems, the measurement frequency is high enough so that the correlation cannot be ignored without degrading tracking performance. In this thesis, target tracking problem with correlated measurement noise is considered. The correlated measurement noise is modeled by a first-order Markov model. The effect of correlation is thought as interference, and Optimum Decoding Based Smoothing Algorithm is applied. For linear models, the estimation performances of Optimum Decoding Based Smoothing Algorithm are compared with the performances of Alpha-Beta Filter Algorithm. For nonlinear models, the estimation performances of Optimum Decoding Based Smoothing Algorithm are compared with the performances of Extended Kalman Filter by performing various simulations.

Existe uma variedade de modelos de dispersão de poluentes, em geral, os modelos gaussianos são usados em todo o mundo por agências ambientais com intuito de regulação. O modelo CALPUFF é um deles. Neste estudo, _e avaliada a influência de escalas de tempo de descorrelação no sistema de modelagem CALPUFF, sob condições atmosféricas neutras. Para fazer isso uma nova parametrização das escalas de tempo descorrelação é proposta. Uma distribuição espectral de um perfil de velocidade euleriana e uma for- mutação da evolução das escalas temporais de descorrelação Lagrangiana são utilizadas como os mecanismos forçantes na dispersão turbulenta, numa camada limite dominada pelo cisalhamento do vento. O desempenho do modelo foi estabelecido com a comparação das concentrações superficiais do experimento Over-Land Alongwind Dispersion. Emissões de fontes em linha foram avaliadas com o modelo CALPUFF com distintas formas de inicialização. Um segundo modelo também foi testado, normalmente utilizado para estudar e prever o impacto ambiental e validar parametrizações turbulentas. É o modelo estocástico de partículas Lagrangiano LAMBDA. Também neste estudo, os resultados do modelo LAMBDA e CALPUFF enfatizam a capacidade da nova derivação de escalas de tempo em representar o comportamento estocástico desconhecido do fenômeno da dispersão de poluentes. / There exists a variety of pollution of dispersion models and in general, Gaussian models are used worldwide by environmental agencies in regulatory applications. The CALPUFF model is one of them. In this study, the in uence of decorrelation time scales in the CALPUFF modeling system under neutral conditions is evaluated. To do this a new parameterization of decorrelation time scales is proposed. A spectral distribution of an Eulerian velocity pro le and a formulation of the evolution of the Lagrangian decorrela- tion timescales are used as the forcing mechanisms (shear-dominated boundary layer) for the turbulent dispersion. The model performance was established by comparing ground- level concentrations with Over-Land Alongwind Dispersion experimental results. Line source emissions was evaluated using the CALPUFF model with different forms of the initialization. A second model was also tested, normally used to study and predict the environmental impact and validate turbulent parameterizations. Is the stochastic La- grangian dispersion model LAMBDA (Ferrero and Anfossi, 1998). Also in this study the model LAMBDA and CALPUFF results emphasized the ability of the new derivation of decorrelation time scales to represent the unknown stochastic behavior.

Existe uma variedade de modelos de dispersão de poluentes, em geral, os modelos gaussianos são usados em todo o mundo por agências ambientais com intuito de regulação. O modelo CALPUFF é um deles. Neste estudo, _e avaliada a influência de escalas de tempo de descorrelação no sistema de modelagem CALPUFF, sob condições atmosféricas neutras. Para fazer isso uma nova parametrização das escalas de tempo descorrelação é proposta. Uma distribuição espectral de um perfil de velocidade euleriana e uma for- mutação da evolução das escalas temporais de descorrelação Lagrangiana são utilizadas como os mecanismos forçantes na dispersão turbulenta, numa camada limite dominada pelo cisalhamento do vento. O desempenho do modelo foi estabelecido com a comparação das concentrações superficiais do experimento Over-Land Alongwind Dispersion. Emissões de fontes em linha foram avaliadas com o modelo CALPUFF com distintas formas de inicialização. Um segundo modelo também foi testado, normalmente utilizado para estudar e prever o impacto ambiental e validar parametrizações turbulentas. É o modelo estocástico de partículas Lagrangiano LAMBDA. Também neste estudo, os resultados do modelo LAMBDA e CALPUFF enfatizam a capacidade da nova derivação de escalas de tempo em representar o comportamento estocástico desconhecido do fenômeno da dispersão de poluentes. / There exists a variety of pollution of dispersion models and in general, Gaussian models are used worldwide by environmental agencies in regulatory applications. The CALPUFF model is one of them. In this study, the in uence of decorrelation time scales in the CALPUFF modeling system under neutral conditions is evaluated. To do this a new parameterization of decorrelation time scales is proposed. A spectral distribution of an Eulerian velocity pro le and a formulation of the evolution of the Lagrangian decorrela- tion timescales are used as the forcing mechanisms (shear-dominated boundary layer) for the turbulent dispersion. The model performance was established by comparing ground- level concentrations with Over-Land Alongwind Dispersion experimental results. Line source emissions was evaluated using the CALPUFF model with different forms of the initialization. A second model was also tested, normally used to study and predict the environmental impact and validate turbulent parameterizations. Is the stochastic La- grangian dispersion model LAMBDA (Ferrero and Anfossi, 1998). Also in this study the model LAMBDA and CALPUFF results emphasized the ability of the new derivation of decorrelation time scales to represent the unknown stochastic behavior.

Cette thèse comporte deux parties qui correspondent à deux domaines distincts : les opérateurs aléatoires et les opérateurs périodiques en dimension 1. Dans la première partie, nous prouvons une estimée de décorrélation pour un opérateur aléatoire avec désordre hors diagonal en dimension 1. En se servant de cette estimée, nous déduisons l'indépendance asymptotique des statistiques locales des valeurs propres près d'énergies distinctes positives dans le régime localisé. Finalement, nous donnons une démonstration alternative de l'estimée de décorrélation pour le modèle d'Anderson discret unidimensionnel. La deuxième partie de cette thèse est liée à un problème de résonances pour l'opérateur de Schrödinger discret en dimension 1 avec potentiel périodique tronqué [...]. / This thesis consists of two parts : te random and periodic operators in dimension 1. In this part, we prove the decorrelation estimate for a 1D lattice Hamiltonian with off-diagonal disorder. Consequently, we deduce the asymptotic independance of the local level statistics near distinct positive energies in the localized regime. Finally, we revisit a known result on the decorrelation estimate for the 1D discret Anderson model. The second part on my thesis adresses questions on resonances for a 1D Schrödinger operators with truncated periodic potential [...].

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Cette thèse concerne la restauration aveugle d’images (formulée comme un problème inverse mal-posé et mal-conditionné), en considérant particulièrement les systèmes SIMO. Dans un premier temps une technique d’identification aveugle de ce système où l’ordre du canal est inconnu (surestimé) est introduite. Nous introduisons d’abord une version simplifiée à coût réduit SCR de la méthode des relations croisées (CR). Ensuite, une version robuste R-SCR basée sur la recherche d’une solution parcimonieuse minimisant la fonction de coût CR est proposée. La restauration d’image est ensuite assurée par une nouvelle approche inspirée des techniques de décodage des signaux 1D et étendue ici aux cas de la restauration d’images en se basant sur une recherche arborescente efficace (algorithme ‘Stack’). Plusieurs améliorations de la méthode ‘Stack’ ont été introduites afin de réduire sa complexité et d’améliorer la qualité de restauration lorsque les images sont fortement bruitées. Ceci en utilisant une technique de régularisation et une approche d’optimisation all-at-once basée sur la descente du gradient qui permet de raffiner l’image estimée et mieux converger vers la solution optimale. Ensuite, les mesures de la qualité d’images sont utilisées comme fonctions de coûts (intégrées dans le critère global) et ce afin d’étudier leur potentiel pour améliorer les performances de restauration. Dans le contexte où l’image d’intérêt est corrompue par d’autres images interférentes, sa restauration nécessite le recours aux techniques de séparation aveugle de sources. Pour cela, une étude comparative de certaines techniques de séparation basées sur la propriété de décorrélation au second ordre et la parcimonie est réalisée. / This thesis concerns the blind restoration of images (formulated as an ill-posed and illconditioned inverse problem), considering a SIMO system. Thus, a blind system identification technique in which the order of the channel is unknown (overestimated) is introduced. Firstly, a simplified version at reduced cost SCR of the cross relation (CR) method is introduced. Secondly, a robust version R-SCR based on the search for a sparse solution minimizing the CR cost function is proposed. Image restoration is then achieved by a new approach (inspired from 1D signal decoding techniques and extended here to the case of 2D images) based on an efficient tree search (Stack algorithm). Several improvements to the ‘Stack’ method have been introduced in order to reduce its complexity and to improve the restoration quality when the images are noisy. This is done using a regularization technique and an all-at-once optimization approach based on the gradient descent which refines the estimated image and improves the algorithm’s convergence towards the optimal solution. Then, image quality measurements are used as cost functions (integrated in the global criterion), in order to study their potential for improving restoration performance. In the context where the image of interest is corrupted by other interfering images, its restoration requires the use of blind sources separation techniques. In this sense, a comparative study of some separation techniques based on the property of second-order decorrelation and sparsity is performed.