This master’s thesis deals with issues, which are suitable to solve by the method of adaptive filtering of additive noise in image processing. It deduces an algorithm of the adaptive filtering method. Then it studies properties of this filter. In the end it applies deduced algorithm on a particular picture and compares the results with linear filtering.

Esse trabalho contempla o estudo sobre o estimador de mínimos quadrados obtido para sistemas lineares discretos sujeitos a ruídos aditivos e a ruídos multiplicativos em seus parâmetros. Supõe-se, adicionalmente, que os parâmetros do sistema estão sujeitos a saltos Markovianos, e que a cadeia de Markov não é conhecida. A solução do problema, sob essas hipóteses, é uma inovação apresentada nesse trabalho. Sob as mesmas hipóteses, o caso estacionário também foi contemplado, e o trabalho apresenta uma demonstração para a convergência da matriz de covariância dos erros do estimador a um valor estacionário, supondo-se estabilidade do sistema e ergodicidade da cadeia de Markov associada. Mostra-se, também, que existe uma única solução positiva semi-definida para a equação de Riccati estacionária e, ainda mais, que tal solução é o limite da matriz de covariância dos erros. A partir da introdução de uma hipótese adicional - de que os parâmetros do sistema estão sujeitos a incertezas na forma de politopos convexos - constrói-se um filtro linear dinâmico em que as iterações possuem estabilidade na média quadrática e que minimiza o limitante superior para o valor esperado do erro quadrático. Uma formulação do tipo LMI (Linear Matrix Inequalities) é proposta para a solução do problema. / This thesis deals with the linear filtering problem for discrete-time Markov jump linear systems with both additive and multiplicative noises. It is assumed that the values of the Markov chain are not available. This is the first time that a solution to the problem with these parameters is presented. By using some usual geometric arguments it is obtained a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the associated Lyapunov and Riccati like equations is presented. By adding an additional hypotesis - that the parameters of the systems are subject to convex polytopic uncertainties - it was designed a dynamic linear filter such that the closed loop system is mean square stable and minimizes an upper bound for the stationary expected value of the square error. A Linear Matrix Inequalities (LMI) formulation is proposed to solve the problem.

Esse trabalho contempla o estudo sobre o estimador de mínimos quadrados obtido para sistemas lineares discretos sujeitos a ruídos aditivos e a ruídos multiplicativos em seus parâmetros. Supõe-se, adicionalmente, que os parâmetros do sistema estão sujeitos a saltos Markovianos, e que a cadeia de Markov não é conhecida. A solução do problema, sob essas hipóteses, é uma inovação apresentada nesse trabalho. Sob as mesmas hipóteses, o caso estacionário também foi contemplado, e o trabalho apresenta uma demonstração para a convergência da matriz de covariância dos erros do estimador a um valor estacionário, supondo-se estabilidade do sistema e ergodicidade da cadeia de Markov associada. Mostra-se, também, que existe uma única solução positiva semi-definida para a equação de Riccati estacionária e, ainda mais, que tal solução é o limite da matriz de covariância dos erros. A partir da introdução de uma hipótese adicional - de que os parâmetros do sistema estão sujeitos a incertezas na forma de politopos convexos - constrói-se um filtro linear dinâmico em que as iterações possuem estabilidade na média quadrática e que minimiza o limitante superior para o valor esperado do erro quadrático. Uma formulação do tipo LMI (Linear Matrix Inequalities) é proposta para a solução do problema. / This thesis deals with the linear filtering problem for discrete-time Markov jump linear systems with both additive and multiplicative noises. It is assumed that the values of the Markov chain are not available. This is the first time that a solution to the problem with these parameters is presented. By using some usual geometric arguments it is obtained a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the associated Lyapunov and Riccati like equations is presented. By adding an additional hypotesis - that the parameters of the systems are subject to convex polytopic uncertainties - it was designed a dynamic linear filter such that the closed loop system is mean square stable and minimizes an upper bound for the stationary expected value of the square error. A Linear Matrix Inequalities (LMI) formulation is proposed to solve the problem.

Statistical Process Control (SPC), and in particular control charting, is widely used to achieve and maintain control of various processes in manufacturing. A control chart is a graphical display that plots quality characteristics versus the sample number or the time line. Interest in effective implementation of control charts for autocorrelated processes has increased in recent years. However, because of the complexities involved, few systematic design approaches have thus far been developed. Many control charting methods can be viewed as the charting of the output of a linear filter applied to the process data. In this dissertation, we generalize the concept of linear filters for control charts and propose new control charting schemes, the general linear filter (GLF) and the 2nd-order linear filter, based on the generalization. In addition, their optimal design methodologies are developed, where the filter parameters are optimally selected to minimize the out-of-control Average Run Length (ARL) while constraining the in-control ARL to some desired value. The optimal linear filters are compared with other methods in terms of ARL performance, and a number of their interesting characteristics are discussed for various types of mean shifts (step, spike, sinusoidal) and various ARMA process models (i.i.d., AR(1), ARMA(1,1)). Also, in this work, a new discretization approach for substantially reducing the computational time and memory use for the Markov chain method of calculating the ARL is proposed. Finally, a gradient-based optimization strategy for searching optimal linear filters is illustrated.

An algorithm that is capable of estimating the parameters of non-stationary sinusoids in real-time lends application to various branches of engineering. Non-stationary sinusoids are sinusoidal signals with time-varying parameters. In this dissertation, a nonlinear filter is applied to power system applications to test its performance. The filter has a structure which renders it fully adaptive to tracking time variations in the parameters of the targeted sinusoid, including its phase and frequency. Mathematical properties of the differential equations which govern the proposed filter are presented. The performance of the proposed filter in the field of power systems is demonstrated with the aid of computer simulations and practical experimentations. The filter is applied to synchronous generator excitation control, voltage dip mitigation as well as the real-time estimation of symmetrical components. The parameter settings of the filter are tested and optimized for each of the applications. This dissertation demonstrates the simulation and experimental results of the filter when applied to the various power system applications. AFRIKAANS : 'n Filter wat bevoeglik is met die beraming van die parameters van beweeglike sinusoïdale in ware-tyd, kan bruikbaar aangewend word in verskeie takke van ingenieurswese. Beweeglike sinuskrommes is sinusoïdale seine met tyd-wisselende parameters. In hierdie verhandeling word `n nie-liniêre filter aangewend in verskeie kragstelseltoepassings om die werksverrigting van die filter te toets. Die filter het 'n struktuur wat dit toelaat om wisselende tydvariasies in die parameters van die teikensinusoïdaal op te spoor, insluitende die fase en frekwensie. Wiskundige eienskappe van die differensiaalvergelykings wat die voorgestelde filter beheer is ondersoek. Die werksverrigting van die voorgestelde filter in die veld van kragstelsels is gedemonstreer met die hulp van rekenaarsimulasies asook praktiese eksperimente. Die filter is toegepas tot opgewekte, sinkrone eksitasie-beheer, spanningsverlaging versagting, asook die ware tyd estimasie van simmetriese komponente. Die parameter verstellings van die filter is getoets en geoptimeer vir elk van die toepassings. Hierdie verhandeling demonstreer die simulering en eksperimentele resultate van die filter wat aangewend is vir verskeie kragstelseltoepassings. Copyright / Dissertation (MSc)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

Ultrasound investigation is one of meaningful imaging at present. Advantages of ultrasound are, that it hasn´t side effects as a rtg radiation and it is noninvasive. Ultrasound diagnostic is exploited in all branch of medicine (urology, cardiology, orthopeadist, gynecology etc.) to display organs, tissues and cavities of the human body. We use display in 2D, 3D and most modern display in 4D. We can encounter with many kinds of artifact. Artifacts are described more closely at 3rd chapter. Speckle noise deteriorates informative yiled of ultrasound picture. We try to remove speckle noise by simpler methods or more complex methods of filtration. These methods are described at 5th chapter. Programme for speckle filtering from pictures is part of this master´s thesis.