This thesis studies a family of unsupervised learning algorithms called feature distribution learning and their extension to perform covariate shift adaptation. Unsupervised learning is one of the most active areas of research in machine learning, and a central challenge in this field is to develop simple and robust algorithms able to work in real-world scenarios. A traditional assumption of machine learning is the independence and identical distribution of data. Unfortunately, in realistic conditions this assumption is often unmet and the performances of traditional algorithms may be severely compromised. Covariate shift adaptation has then developed as a lively sub-field concerned with designing algorithms that can account for covariate shift, that is for a difference in the distribution of training and test samples. The first part of this dissertation focuses on the study of a family of unsupervised learning algorithms that has been recently proposed and has shown promise: feature distribution learning; in particular, sparse filtering, the most representative feature distribution learning algorithm, has commanded interest because of its simplicity and state-of-the-art performance. Despite its success and its frequent adoption, sparse filtering lacks any strong theoretical justification. This research questions how feature distribution learning can be rigorously formalized and how the dynamics of sparse filtering can be explained. These questions are answered by first putting forward a new definition of feature distribution learning based on concepts from information theory and optimization theory; relying on this, a theoretical analysis of sparse filtering is carried out, which is validated on both synthetic and real-world data sets. In the second part, the use of feature distribution learning algorithms to perform covariate shift adaptation is considered. Indeed, because of their definition and apparent insensitivity to the problem of modelling data distributions, feature distribution learning algorithms seems particularly fit to deal with covariate shift. This research questions whether and how feature distribution learning may be fruitfully employed to perform covariate shift adaptation. After making explicit the conditions of success for performing covariate shift adaptation, a theoretical analysis of sparse filtering and another novel algorithm, periodic sparse filtering, is carried out; this allows for the determination of the specific conditions under which these algorithms successfully work. Finally, a comparison of these sparse filtering-based algorithms against other traditional algorithms aimed at covariate shift adaptation is offered, showing that the novel algorithm is able to achieve competitive performance. In conclusion, this thesis provides a new rigorous framework to analyse and design feature distribution learning algorithms; it sheds light on the hidden assumptions behind sparse filtering, offering a clear understanding of its conditions of success; it uncovers the potential and the limitations of sparse filtering-based algorithm in performing covariate shift adaptation. These results are relevant both for researchers interested in furthering the understanding of unsupervised learning algorithms and for practitioners interested in deploying feature distribution learning in an informed way.

The volatility of house prices can raise systemic risks in the housing market due to the vulnerability of the banking and mortgage sectors to such fluctuations. Moreover, the extreme increases in housing markets have been considered a key feature of the last economic crisis and the run-up to it. Such increases, however, came to a sudden halt immediately before the crisis or directly it began. Despite the recent growth of scholarly work on the role of house price behaviour in economic stability, fundamental questions have yet to be answered: for instance: (i) how far do the nonlinear models outperform the linear models? And how does such nonlinearity explain the asymmetry in the cycle; (ii) what are the main characteristics of house price cycles, and how do they differ over time; and (iii) what kind of policy intervention would stop a real estate boom? This thesis, made up of three empirical essays, aims to take a step forward in answering these questions. The first essay examines whether house prices in large metropolitan areas such as London, New York and Hong Kong follow linear or nonlinear models. The Smooth Transition Autoregressive model was used on a sample of monthly data over the period 1996:1 to 2015:12. The results indicate that linear models are unsuitable for modelling the housing market for the chosen cities. Moreover, strong evidence indicates that real estate prices are largely nonlinear and can well be modelled using a logistic smooth transition model (LSTAR). Estimation results also show different degrees of asymmetry. In particular, the speed of transition between the expansion and contraction of house prices is greater in London than it is in Hong Kong while the speed of transition between boom and bust in New York house prices is the slowest. Further, the forecast results suggest that the LSTAR outdoes the linear model in out-of-sample performance. The second essay investigates the main features of house price cycles in the same major metropolitan areas by providing a reasonable level of discrimination between the cyclical decomposition techniques available for capturing suitable measurements for house price cycles. Through a sample of large cities in several countries, it is shown that the model-based filter is suitable for capturing the main features of house price cycles and the results confirm that these cycles are centred at low frequency. Moreover, there is evidence of substantial variation in the duration and amplitude of these cycles both across cities and over time. The third essay provides evidence that real house prices are significantly affected by financial stability policies. Considering the Hong Kong experience, the results show strong evidence of duration dependences in both the upswing and downswing phases of the cycle. Moreover, the time taken to reach the turning point increases dramatically as the cycle proceeds. The findings also suggest that there is feedback between house price volatility and the policies that affect the housing market. Accordingly, house prices respond with more volatility to any change in the loan to value and lending policy indicators (ignoring the sign of this shock). Finally, the evidence of asymmetry suggests that unanticipated house price increases are more destabilising than unanticipated falls in house prices.

Thesis. 1977. Ocean E.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Ocean E.

Thesis. 1977. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Bibliography : leaves 127-133. / M.S.

A presente dissertação traz reflexões sobre os processos de gentrificação combinando argumentações teóricas baseadas em modelos teóricos que preveem analises fundamentadas em oferta e demanda, e através da renda diferencial que possibilita a analise de um potencial de renda, unindose a teorias de deslocamento, teoria de filtragem e teoria do ciclo de vida familiar, assim como atrair para discussão teorias sobre centro e subcentros. Com esses conceitos sugere-se uma analise que transpasse o processo de gentrificação, observando qual a consequência do processo efetivado e com quais fenômenos ele pode vir a contribuir , assim como também, se observa quais fenômenos podem contribuir para que o processo de gentrificação ocorra. Após essas conceituações, apresentar-se-ão exemplos de processos de gentrificação, apresentados sobre a perspectiva de seus pesquisadores contribuindo, para uma compreensão mais abrangente sobre as causas e efeitos abordados no processo de gentrificação, através da percepção de suas características expostas em diversos casos que possuem espaços constituídos de forma única. Para assim conseguir-se uma base substancial na procura por indícios de processos da primeira e da segunda onda do processo de gentrifcação no município de São Paulo. / The present dissertation brings reflections on the processes of gentrification combining theoretical arguments based on theoretical models that foresee analyzes based on supply and demand, and through rent gap that allows the analysis of an income potential, joining theories of displacement, theory Filtering and family life cycle theory, as well as to attract theories about the center and subcenters for discussion. With these concepts, it is suggested an analysis that transcends the process of gentrification, observing the consequences of the actual process and with which phenomena it may contribute, as well as observing which phenomena may contribute to the process of gentrification occurring. After these conceptualizations, we will present examples of gentrification processes, presented on the perspective of their researchers, contributing to a more comprehensive understanding of the causes and effects addressed in the gentrification process, through the perception of their characteristics exposed in several cases which have uniquely shaped spaces. In order to obtain a substantial base in the search for indications of processes of the first and second waves of the process of gentrification in the city of São Paulo.

A reconstrução tomográfica de imagens com ruído Poisson tem grandes aplicações em medicina nuclear. A demanda por informações mais complexas, como por exemplo, várias secções de um órgão, e a necessidade de reduzir a dosagem radioativa a que o paciente é submetido, requerem métodos adequados para a reconstrução de imagem com baixa contagem, no caso, baixa relação sinal/ruído. A abordagem estatística, utilizando a máxima verossimilhança (ML) e o algoritmo Expectation-Maximization (EM), produz melhores resultados do que os métodos tradicionais, pois incorpora a natureza estatística do ruído no seu modelo. A presente tese apresenta uma solução alternativa, considerando também o modelo de ruído Poisson, que produz resultados comparáveis ao do ML-EM, porém com custo computacional bem menor. A metodologia proposta consiste, basicamente, em se estimar as projeções considerando o modelo de formação das projeções ruidosas, antes do processo da reconstrução. São discutidos vários estimadores otimizados, inclusive Bayesianos. Em especial, é mostrado que a transformação de ruído Poisson em ruído aditivo Gaussiano e independente do sinal (transformação de Anscombe), conjugada à estimativa, produz bons resultados. Se as projeções puderem ser consideradas, aproximadamente, transformadas de Radon da imagem a ser reconstruída, então pode ser aplicado um dos métodos da transformada para a reconstrução tomográfica. Dentre estes métodos, o da aplicação direta da transformada de Fourier foi avaliado mais detalhadamente devido ao seu grande potencial para reconstruções rápidas com processamento vetorial e processamento paralelo. A avaliação do método proposto foi realizada através de simulações, onde foram geradas as imagens originais e as projeções com ruído Poisson. Os resultados foramcomparados com métodos clássicos como a filtragem-retroprojeção, o ART e o ML-EM. Em particular, a transformação de Anscombe conjungada ao estimador heurístico (filtro de Maeda), mostrou resultados próximos aos do ML-EM, porém com tempo de processamento bem menor. Os resultados obtidos mostram a viabilidade da presente proposta vir a ser utilizada em aplicações clínicas na medicina nuclear. / Tomographic reconstruction of images with Poisson noise is in important problem in nuclear medicine. The need for more complete information, like the reconstruction of several sections of an organ, and the necessity to reduce patient absorbed radioactivity, suggest better methods to reconstruct images with low-count and low signal-to-noise ratio. Statistical approaches using Maximum Likelihood (ML) and the Expectation-Maximization (EM) algorithm lead to better results than classical methods, since ML-EM considers in its model the stochastic nature of the noise. This thesis presents an alternative solution, also using a Poisson noise model, that produces similar results as compared to ML-EM, but with much less computational cost. The proposed technique basically consists of projection estimation before reconstruction, taking into account a model for the formation of the noisy projections. Several optimal and Bayesian estimators are analysed. It is shown that the transformation of Poisson noise into Gaussian additive and independent noise (Anscombe Transformation), followed by estimation, yields good results. If the projection can be assumed as Radon transform of the image to be reconstructed, then it is possible to reconstruct using one of the transform methods. Among these methods, the Direct Fourier Method was analysed in detail, due to its applicability for fast reconstruction using array processors and parallel processing. Computer simulations were used in order to access this proposed technique. Phantoms and phantom projections with Poisson noise were generated. The results were compared with traditional methods like Filtering-Backprojection, Algebraic Rconstruction Technique (ART) and ML-EM. Specifically, the Anscombe transformation together with a heuristic estimator (Maeda\'s filter) produced results comparable to ML-EM, but spending only a fraction of the processing time.

Neste trabalho faz-se um estudo sobre filtros IIR adaptativos e é apresentada uma estrutura polifásica para filtragem IIR adaptativa, que, em troca de um aumento de complexidade computacional, pode apresentar características mais favoráveis do que a estrutura direta comumente usada. O aumento da complexidade computacional, relativamente a um algoritmo do tipo newton, por exemplo, é pequeno. Apresenta-se uma análise dos efeitos da proximidade ao círculo unitário dos pólos do sistema sendo modelado. Um dos efeitos considerados é o comportamento limite do condicionamento da matriz de estados associada ao algoritmo de adaptação. São considerados algoritmos de adaptação de passo constante de uso comum para filtros IIR adaptativos. O método utilizado é particularmente útil para a verificação do efeito da posição dos pólos do sistema sendo modelado e também para a introdução de certas restrições ao mesmo, como, por exemplo, norma L2 fixa e resposta em freqüência passa-tudo. Um resultado interessante é que a única situação, entre as testadas, em que o condicionamento da matriz mencionada não tende a infinito quando um número qualquer de polosndo sistema sendo modelado H(z) se aproxima da circunferência unitária, é quando H(z) é passa-tudo e emprega-se o algoritmo PLR. São analisadas também a superfície de erro e a superfície de erro reduzida para filtros IIR adaptativos. Mostra-se que, quando o sistema sendo modelado possui polos próximos à circunferência unitária, a superfície de erro reduzida apresenta regiões planas com erro quadrático médio elevado. A existência destas regiões resulta em uma baixa velocidade de convergência global de algoritmos de passo constante. A partir da decomposição em valores singulares (SVD) da forma de Hankel do sistema sendo modelado, é apresentada também uma decomposição da superfície de erro reduzida, a partir da qual pode-se obter uma separaçãoparcial dos efeitos do sistema sendo modelado e da forma de realização do filtro adaptativo. Uma estrutura polifásica para filtragem IIR adaptativa é apresentada e seu desempenho é comparado com o de filtros IIR adaptativos na forma direta. Mostra-se o possível ganho da estrutura polifásica quanto à velocidade de convergência local e quanto às características da superfície de erro reduzida e à velocidade de convergência global. Demonstra-se, para a estrutura polifásica, que, com entrada branca e modelamento suficiente, todos os pontos estacionários da superfície de erro são mínimos globais da mesma. Este resultado não decorre diretamente de propriedades análogas relativas à estrutura direta, já conhecidas. Tudo para a estrutura direta quanto para a estrutura polifásica, são apresentados os resultados de várias simulações dos algoritmos de adaptação considerados. / A study on IRR adaptive filters and polyphase structure for IIR adaptive filtering are presented. In exchange for an increase in computational complexity, which is small if compared to Newton algorithms, the polyphaser structure may exhibit a better performance than direct structures. An analysis of the effects of the proximity to the unit circle of the modelled system\'s poles is presented. One of the considered points is the limiting behavior of the condition of the state matrix related to the adaptive algorithm. Commonly used constant gain algorithms are considered. The method of analysis is specially usefull for verifying the effects of the position of the system\'s poles and also for introducing certain restrictions to the system, as fixed L2 norm and all-pass frequency response. An interesting result is that, among the situations that were tested, the only one in which the condition of the aforementioned matrix does not tend to infinity as the poles of the modelled system H(z) tend to the unit circle is when H)z) is all-pass and the PLR algorithm is employed. The error surface and the reduced error surface for IIR adaptive filters are also analyzed. It is shown that the modelled system has poles close to the unit circle the reduced error surface presents flat regions with high mean square error. The presence of these flat regions results in low global convergence speed for constant gain adaptive algorithms. Based on the singular value decomposition (SVD) of the modelled system\'s Hankel form, a decomposition of the reduced error surface is also presented. In it there exists a partial separation of the effects of the system and the adaptive filter\'s structure. A polyphaser structure for IIR adaptive filtering is presented and its performance is compared to the performance of the direct structure. The gain in local convergence and global convergencespeed, as well as the better behavior of the reduced error surface which may be attained , are shown. It is demonstrated, for the polyphaser structure, that, with while input and sufficient modelling, all the stationary points of the error surface are global minima. This result does not follow directly from similar well known results for the direct structure. Simulation results for the considered algorithms are also presented.

As one of the social relations, "distrust" also performs an important role in online Web sites. We also observe that distrust information can also be incorporated to improve recommendation quality. Hence, the last part of this thesis studies the problem on how to improve recommender system by considering explicit distrust information among users. We make the assumption that users' distrust relations can be interpreted as the "dissimilar" relations since user ui distrusts user ud indicates that user ui disagrees with most of the opinions issued by user ud. Based on this intuition, the distrust relations between users can be easily modeled by adding the regularization term into the objective functions of the user-item matrix factorization. The experiments on the Epinions dataset indicate that distrust information is at least as important as trust information. / However, the data sparsity problem of the involved user-item matrix seriously affects the recommendation quality. Many existing approaches to recommender systems cannot easily deal with users who have made very few ratings. The objective of this thesis is to study how to build effective and efficient approaches to improve the recommendation performance. / In this thesis, we first propose two collaborative filtering methods which only utilize the user-item matrix for recommendations. The first method is a neighborhood-based collaborative filtering method which designs an effective missing data prediction algorithm to improve recommendation quality, while the second one is a model-based collaborative filtering method which employs matrix factorization technique to make the recommendation more accurate. / In view of the exponential growth of information generated by online users, social contextual information analysis is becoming important for many Web applications. Hence, based on the assumption that users can be easily influenced by the friends they trust and prefer their friends' recommendations, we propose two recommendation algorithms by incorporating users' social trust information. These two methods are based on probabilistic matrix factorization. The complexity analysis indicates that our approaches can be applied to very large datasets since they scale linearly with the number of observations, while the experimental results show that our methods perform better than the state-of-the-art approaches. / Recommender Systems are becoming increasingly indispensable nowadays since they focus on solving the information overload problem, by providing users with more proactive and personalized information services. Typically, recommender systems are based on Collaborative Filtering, which is a technique that automatically predicts the interest of an active user by collecting rating information from other similar users or items. Due to their potential commercial values and the associated great research challenges, Recommender systems have been extensively studied by both academia and industry recently. / Ma, Hao. / "December 2009." / Advisers: Irwin King; Michael R. Lyu. / Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 136-154). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Tsang, Chi Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 66-69). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Statement of Originality --- p.v / Table of Contents --- p.vii / List of Figures --- p.x / Nomenclature --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Objectives --- p.3 / Chapter 1.3 --- Contributions --- p.3 / Chapter 1.4 --- Thesis Organization --- p.4 / Chapter 2 --- A Ubiquitous Digital Writing System --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- MEMS Motion Sensing Technology --- p.6 / Chapter 2.2.1 --- Micro-Electro-Mechanical Systems (MEMS) --- p.6 / Chapter 2.2.2 --- Principle of a MEMS Accelerometer --- p.6 / Chapter 2.2.3 --- Principle of a MEMS Gyroscope --- p.7 / Chapter 2.3 --- Architecture of Ubiquitous Digital Writing System --- p.8 / Chapter 2.3.1 --- Micro Inertial Measurement Unit (μlMU) --- p.8 / Chapter 2.3.2 --- Data Transmission Module --- p.10 / Chapter 2.3.3 --- User Interface Software --- p.10 / Chapter 2.4 --- Summary --- p.12 / Chapter 3 --- Calibration of μ-Inertial Measurement Unit --- p.13 / Chapter 3.1 --- Introduction --- p.13 / Chapter 3.2 --- Sources of Error --- p.13 / Chapter 3.2.1 --- Deterministic Errors --- p.13 / Chapter 3.2.2 --- Stochastic Error --- p.14 / Chapter 3.3 --- Calibration of Accelerometers --- p.14 / Chapter 3.4 --- Coordinate Transformation with Gravity Compensation --- p.15 / Chapter 3.4.1 --- Coordinate Transformation --- p.16 / Chapter 3.4.2 --- Attitude Determination --- p.18 / Chapter 3.4.3 --- Gravity Compensation --- p.19 / Chapter 3.5 --- Summary --- p.20 / Chapter 4 --- Zero Velocity Compensation --- p.21 / Chapter 4.1 --- Introduction --- p.21 / Chapter 4.2 --- Algorithm Description --- p.21 / Chapter 4.2.1 --- Stroke Segmentation --- p.22 / Chapter 4.2.2 --- Zero Velocity Compensation (ZVC) --- p.22 / Chapter 4.3 --- Experimental Results and Discussion --- p.23 / Chapter 4.4 --- Summary --- p.24 / Chapter 5 --- Kalman Filtering --- p.28 / Chapter 5.1 --- Introduction --- p.28 / Chapter 5.2 --- Summary of Kalman filtering algorithm --- p.28 / Chapter 5.2.1 --- System Model --- p.28 / Chapter 5.2.2 --- Initialization --- p.29 / Chapter 5.2.3 --- Time Update --- p.32 / Chapter 5.2.4 --- Measurement Update --- p.33 / Chapter 5.2.5 --- Stroke Segmentation --- p.34 / Chapter 5.3 --- Summary --- p.34 / Chapter 6 --- Error Compensation from Position Feedback --- p.35 / Chapter 6.1 --- Introduction --- p.35 / Chapter 6.2 --- Global Positioning System (GPS) --- p.35 / Chapter 6.3 --- Zero z-axis Kalman Filtering --- p.36 / Chapter 6.3.1 --- Algorithm Implementation --- p.36 / Chapter 6.3.2 --- Experimental Results and Discussion --- p.40 / Chapter 6.4 --- Combined Electromagnetic Resonance (EMR) Position Detection Board and μlMU --- p.43 / Chapter 6.4.1 --- EMR Position Detection System --- p.43 / Chapter 6.4.2 --- A Combined Scheme --- p.44 / Chapter 6.4.3 --- Algorithm Implementation --- p.46 / Chapter 6.4.4 --- Synchronization --- p.50 / Chapter 6.4.5 --- Experimental Results and Discussion --- p.50 / Chapter 6.5 --- Summary --- p.54 / Chapter 7 --- Conclusion --- p.55 / Chapter 7.1 --- Future Work --- p.56 / Chapter 7.1.1 --- Improvement in the μlMU --- p.56 / Chapter 7.1.2 --- Combined Camera Optical Tracking and μlMU --- p.57 / Chapter 7.2 --- Concluding Remarks --- p.58 / Chapter A --- Derivation of Kalman Filtering Algorithm --- p.59 / Chapter A.1 --- Introduction --- p.59 / Chapter A.2 --- Derivation of a Priori State Estimation Equation --- p.60 / Chapter A.3 --- Derivation of a Posteriori State Estimation Equation --- p.60 / Chapter A.4 --- Derivation of a Priori Error Covariance Matrix --- p.61 / Chapter A.5 --- Derivation of the Optimal Kalman Gain --- p.62 / Chapter A.6 --- Derivation of a Posteriori Error Covariance Matrix --- p.63 / Chapter B --- Derivation of Process Noise Covariance Matrix --- p.64 / Bibliography --- p.66 / Publications --- p.69

Métodos de suavização através de processos de difusão é frequentemente utilizado como etapa prévia em diferentes procedimentos em imagens. Apesar da difusão anômala ser um processo físico conhecido, ainda não é aplicada à suavização de imagens como a difusão clássica. Esta dissertação propõe e relata a implementação e avaliação de filtros de difusão anômala, tanto isotrópico quanto anisotrópico, como um método de melhoramento em imagens ponderadas em difusão (DWI) e imagens de tensor de difusão (DTI) dentro do imageamento por ressonãncia magnética (MRI). Aqui propõe-se generalizar a difusão anisotrópica e isotrópica com o conceito de difusão anômala em processamento de imagens. Como metodologia implementou-se computacionalmente as equações de difusão bidimensional e aplicou às imagens MRI para avaliar o seu potencial como filtro de melhoramento. Foram utilizadas imagens de ressonância magnética de aquisição DTI em voluntários saudáveis. Os resultados obtidos neste estudo foram a verificação que métodos baseados em difusão anômala melhoram a qualidade em processamento das imagens DTI e DWI quando observadas medidas de qualidade como a relação sinal ruído (SNR) e índice de similaridade estrutural (SSIM), e assim determinou-se parâmetros ótimos para as diferentes imagens e situações que foram avaliadas em função dos seus parâmetros de controle, em especial o parâmetro anômalo, chamado de q. Os resultados apresentados aqui permitem prever não apenas uma melhora na qualidade das imagens DTI e DWI resultantes do processamento proposto, como também possível redução de repetições na sequência de aquisição de MRI para um SNR predeterminado. / Smoothing methods through diffusion processes is often used as a preliminary step in different procedures in images. Although the anomalous diffusion is a known physical process, it is not applied to image smoothing as the classical diffusion. This paper proposes and describes implementation and evaluation of anomalous diffusion filters, both isotropic and anisotropic, as a method of improving on diffusion-weighted images (DWI) and diffusion tensor images (DTI) within the magnetic resonance imaging (MRI). Hereby is proposed to generalize the isotropic and anisotropic diffusion with the concept of anomalous diffusion in image processing. The methodology is implemented computationally as bidimensional diffusion equations and applied to MRI images to evaluate its potential as a filter for quality improvement. We used DTI and DWI imaging to acquire from healthy volunteers as image set. The results of this study verified that methods based on anomalous diffusion improved DWI and DTI image processing when observed quality measures such as signal to noise ratio (SNR) and structural similarity index (SSIM), and determined filter optimal parameters for different images and situations evaluated in terms of their control parameters, particularly the anomalous parameter, called q. The results presented here can predict not only an improvement in the quality of DWI and DTI images resulting from the proposed method, and additionally the possible reduction of repetitions following acquisition of MRI for a predetermined SNR.