Stuttgart, Univ., Studienarbeit, 2006.

[pt] Neste trabalho são estudados os moduladores delta desenvolvido a partir do conhecimento estatístico disponível sobre o sinal a ser transmitido. Estes moduladores são aqui chamados estruturados. Após uma rápida introdução à modulação delta, são descritos alguns sistemas mais conhecidos. Os sistemas estruturados são então formalmente caracterizados e uma análise teórica é desenvolvida, sendo apontadas as dificuldades analíticas envolvidas. A partir de uma configuração básica proposta por C.L. Song, são desenvolvidas equações gerais diferentes das por ele obtidas. A particularização destas equações para sinais Gauss Markov de primeira Ordem dá origem ao chamado sistema Song modificado. Resultados obtidos a partir da simulação digital do sistema de song, do sistema de Song modificado, e do sistema delta simples, são apresentados. Um processo adaptativo para aumentar a faixa dinâmica é proposto com base nos resultados de simulação. / [en] This work examines delta modulation systems in which statistical knowledge about the signal to be tranmitted is explicitly used in sistem design. These modulators are called here structured delta modulators. After a brief introduction to delta modulation some well-known systems are described. Structured systems are then formally defined and analytical difficulties in finding general solutions are pointed out. Starting from a system proposed by C.L. Song, general equations are derived. These equations, which are more complete than the ones obtained by Song are then specialized to first-order Gauss-Maarkov signals, leading to what has been called a modified Song modulators. Digital simulations results are then obtained for song modulators, modified Song modulators and linear delta modulators. An adptive producedure is finally suggested to improve the dynamic range of these systems.

University, Diss., 2007--Bonn.

Thesis (Doctoral)--Ruhr-Universität Bochum, 1983.

[pt] Neste trabalho aplica-se o método de inovações ao problema de estimação de um processo Gauss-Markov provindo de um sistema multivariável descrito por uma equação de estado. Após a dedução das fórmulas gerais de estimação em termos do processo de inovações obtém-se os algoritmos recursivos do filtro de Kalman-Bucy para o caso não linear contínuo, bem como, para o caso linear continuo e discreto. A seguir, faz-se a representação do processo como saída de um sistema causal e causalmente reversível excitado por um ruído branco, chamada representação por inovações (RI). Os parâmetros deste sistema são determinados a partir da covariância do processo. Finalmente, é desenvolvido um algoritmo para a determinação de uma RI de um processo estacionário provindo de um sistema desconhecido, invariante no tempo. / [en] In this work the innovations method is applied to the estimation problem of a Gauss-Markov process, output of a multivariable system described by a state equation. After obtaining general estimation formulas in terms of the innovations process, the Kalman-Bucy filter recursive algorithms are derived for the nonlinear continuous case as well as for the linear discrete and continuous case. Next, it is given a representation of the process as an output of a causal and causally reversible system to a white noise, known as the innovation representation. The parameters of such a system are determined from the process covariance. Finally, an algorithm is built to obtain an IR of a stationary process coming from an unknown time-invariant system.

In this paper, we study the parameter estimation of the multiple linear time series regression model with long memory stochastic regressors and innovations. Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) proposed a class of frequency-domain weighted least squares estimates. Their estimates are shown to achieve the Gauss-Markov bound with standard convergence rate. In this study, we proposed a time-domain generalized LSE approach, in which the inverse autocovariance matrix of the innovations is estimated via autoregressive coefficients. Simulation studies are performed to compare the proposed estimates with Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002). The results show the time-domain generalized LSE is comparable to Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) and attains higher efficiencies when the autoregressive or moving average coefficients of the FARIMA models have larger values. A variance reduction estimator, called TF estimator, based on linear combination of the proposed estimator and Hidalgo and Robinson (2002)'s estimator is further proposed to improve the efficiency. Bootstrap method is applied to estimate the weights of the linear combination. Simulation results show the TF estimator outperforms the frequency-domain as well as the time-domain approaches.

In this thesis, we have a comprehensive study of the famous compound Gauss-Markov image model. In this model, a pixel in the image random field is determined by the surrounding pixels according to a predetermined line field. This model is useful in image restoration by applying two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. CGM (Compound Gauss-Markov) image modeling is characterized by the line fields and the generating noise. In this thesis we apply combinations of techniques such as changing processing order, immediate updating, probability determination and different methods to find the best modeling. Furthermore, the effects of the above modeling are demonstrated by its energy, visual quality, and error resistance. Finally, by solving a set of nonlinear equations we apply the CGM model to an image restoration problem for image corrupted by a dusted lens.

Image modeling is a foundation for many image processing applications. The compound Gauss-Markov (CGM) image model has been proven useful in picture restoration for natural images. In contrast, other Markov Random Fields (MRF) such as Gaussian MRF models are specialized on segmentation for texture image. The CGM image is restored in two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. The line fields are most important for a successful CGM modeling. A convincing line fields should be fair on both fields: horizontal and vertical lines. The working order and update occasions have great effects on the results of line fields in iterative computation procedures. The above two techniques are the basic for our research in finding the best modeling for CGM. Besides, we impose an extra condition for a line to exist to compensate the bias of line fields. This condition is based upon a requirement of a brightness contrast on the line field. Our best modeling is verified by the effect of image restoration in visual quality and numerical values for natural images. Furthermore, an artificial image generated by CGM is tested to prove that our best modeling is correct.

Images are liable to being corrupted by noise when they are processed for many applications such as sampling, storage and transmission. In this thesis, we propose a method of image restoration for image corrupted by a white Gaussian noise. This method is based upon Gauss-Markov random field model combined with a technique of image segmentation. As a result, the image can be restored by MAP estimation. In the approach of Gauss-Markov random field model, the image is restored by MAP estimation implemented by simulated annealing or deterministic search methods. By image segmentation, the region parameters and the power of generating noise can be obtained for every region. The above parameters are important for MAP estimation of the Gauss-Markov Random field model. As a summary, we first segment the image to find the important region parameters and then restore the image by MAP estimation with using the above region parameters. Finally, the intermediate image is restored again by the conventional Gauss-Markov random field model method. The advantage of our method is the clear edges by the first restoration and deblured images by the second restoration.

The restoration of degraded images is one important application of image processing. The classical approach of image restoration, such as low-pass filter method, is usually stressed on the numerical error but with a disadvantage in visual quality of blurred texture. Therefore, a new method of image restoration, based upon image model by Compound Gauss-Markov(CGM) Random Fields, using MAP(maximum a posteriori probability) approach focused on image texture effect has been proved to be helpful. However, the contour of the restored image and numerical error for the method is poor because the conventional CGM model uses fixed global parameters for the whole image. To improve these disadvantages, we adopt the adjustable parameters method to estimate model parameters and restore the image. But the parameter estimation for the CGM model is difficult since the CGM model has 80 interdependent parameters. Therefore, we first adopt the parameter reduction approach to reduce the complexity of parameter estimation. Finally, the initial value set of the parameters is important. The different initial value might produce different results. The experiment results show that the proposed method using adjustable parameters has good numerical error and visual quality than the conventional methods using fixed parameters.