Deep Brain Stimulation (DBS) is a developing therapeutic technique with a high potential to control and treat central nervous system diseases through neuromodulation. DBS utilizes through implanted electrodes that are inserted in the targeted brain structure. Being an emerging technology; neuromodulation introduces many challenges that are not yet comprehensively identified, characterized and resolved. The advancement of this technique requires qualitative and quantitative perception of the brain response to electrical stimulation which is controlled by the electric field distribution within the brain tissue. This can be realized by formulating the tissue-field interaction such that we will have a better understanding of the spatial extent and the direct effects of deep brain stimulation (DBS) on neurons activity. The focus of this research is to develop a model for encoding and decoding the neuron activity in the DBS region and to address all the parameters that affect this activity in order to have a complete understanding of the DBS problem and to develop a brain model that can be readily used in DBS analysis. Our goal is to study the immediate direct effects of the stimulating field and examine where the beneficial effects of DBS originate since the mechanism of DBS is not yet fully understand and hence an inclusive comprehensive performance study will be done for the DBS problem.

Deep Brain Stimulation (DBS) is a developing therapeutic technique with a high potential to control and treat central nervous system diseases through neuromodulation. DBS utilizes through implanted electrodes that are inserted in the targeted brain structure. Being an emerging technology; neuromodulation introduces many challenges that are not yet comprehensively identified, characterized and resolved. The advancement of this technique requires qualitative and quantitative perception of the brain response to electrical stimulation which is controlled by the electric field distribution within the brain tissue. This can be realized by formulating the tissue-field interaction such that we will have a better understanding of the spatial extent and the direct effects of deep brain stimulation (DBS) on neurons activity. The focus of this research is to develop a model for encoding and decoding the neuron activity in the DBS region and to address all the parameters that affect this activity in order to have a complete understanding of the DBS problem and to develop a brain model that can be readily used in DBS analysis. Our goal is to study the immediate direct effects of the stimulating field and examine where the beneficial effects of DBS originate since the mechanism of DBS is not yet fully understand and hence an inclusive comprehensive performance study will be done for the DBS problem.

This thesis discusses image processing and filtering techniques with emphasis on Mean filter, Median filter, and different versions of the Iterative Truncated Arithmetic Mean (ITM) filter. Specifically, we review in detail the ITM algorithms (ITM1 and ITM2) proposed by Xudong Jiang. Although filtering is capable of reducing noise in an image, it usually also results in smoothening or some other form of distortion of image edges and file details. Therefore, maintaining a proper trade off between noise reduction and edge/detail distortion is key. In this thesis, an improvement over Xudong Jiang’s ITM filters, namely ITM3, has been proposed and tested for different types of noise and for different images. Each of the two original ITM filters performs better than the other under different conditions. Experimental results demonstrate that the proposed filter, ITM3, provides a better trade off than ITM1 and ITM2 in terms of attenuating different types of noise and preserving fine image details and edges.

Cuando observamos el cielo con los instrumentos más avanzados en la frecuencia de las microondas, los fotones que vemos fueron originados en regiones muy diferentes del universo. La mayoría proceden de nuestra propia galaxia (emisión difusa de sincrotrón, free-free y polvo), otros se originan en galaxias y cúmulos de galaxias muy lejanos, y, finalmente, una fracción tendrá su origen en la radiación del Big Bang, conocida como la Radiación del Fondo Cósmico de Microondas. Esta radiación está contaminada por las otras y su separación de ellas de una forma satisfactoria sigue siendo un problema abierto. En esta tesis exploraremos diferentes técnicas basadas en filtros lineales para detectar y separar uno de estos contaminantes, la contribución a la señal que se observa de radio galaxias y galaxias infrarrojas lejanas. Éstas son conocidas como fuentes puntuales porque aparecen como objetos puntuales no resueltos -- debido a las típicas resoluciones angulares de los instrumentos usados en los experimentos. En primer lugar, vamos a estudiar las propiedades de una familia de filtros adaptados para la detección de fuentes puntuales, donde modificamos la escala del filtro y usamos un test de Neyman-Pearson para definir la región de aceptación. En segundo lugar, consideramos un nuevo filtro (BSAF) que tiene dos parámetros que se pueden optimizar para maximizar el número de detecciones reales fijado un número de detecciones espurias. En tercer lugar, extendemos el BSAF al caso dos-dimensional y lo comparamos con la ondícula de sombrero mejicano (MHW). En cuarto lugar, estudiamos una nueva técnica de fusión de lineal y cuadrática de imágenes. En quinto lugar, comparamos tres filtros usando simulaciones realistas de Planck. En sexto lugar, para terminar, usamos el segundo miembro de la familia de ondículas de sombrero mejicano para hacer una detección no-ciega en las cinco frecuencias del satélite WMAP, analizando 2491 objetos observados a 5 GHz y produciendo un catálogo de 932 objetos observados a 3σ y 380 a 5σ. / When we observe the sky with the most advanced instruments operating at microwave frequencies, the photons that we see were originated in very different regions in the universe. Most of them come from our own Galaxy (diffuse synchrotron, free-free and dust emission), others come from very distant galaxies and clusters of galaxies, and, finally, a fraction will have their origin in the relic radiation of the Big Bang, known as the Cosmic Microwave Background Radiation. This radiation is contaminated by the other components and the separation of the different emissions in a satisfactory way is still an open problem. In this thesis we will explore different techniques based on linear filters to detect and separate one of the contaminants, the contribution to the observed signal of distant radio and infrared galaxies. These galaxies are known as extragalactic point sources because, for the angular resolution of the typical experiments in microwave frequencies, they appear as point-like unresolved objects. First, we will study the performance of a family of matched filters when detecting point sources, where we allow the scale of the filter to be modified and where we introduce a Neyman-Pearson test to define the region of acceptance. Second, we will consider a new one-dimensional linear filter, the Biparametric Scale-Adaptive Filter (BSAF), that has two parameters that can be optimised to maximise the number of real detections for a fixed number of spurious detections, used in conjuction with a Neyman-Pearson test. Third, we will extend the BSAF to two dimensions, and compare it with the Mexican Hat Wavelet. Fourth, we will explore a new technique that combines lineal and quadratic fusion of images with linear filters, testing it with realistic simulations of one of the Planck satellite channels. Fifth, we will study in detail the performance of three filters, the Matched filter and two members of the Mexican Hat wavelet in realistic simulations of the nine channels of Planck. To conclude, we will use the second member of the Mexican Hat Family to do a non-blind study in the five frequencies of WMAP of a complete sample of 2491 sources observed at 5 GHz, producing a catalogue of 932 objects detected above 3σ and a catalogue of 380 objects observed above 5σ.

Muitos pesquisadores têm se interessado em explorar o vasto poder computacional das recentes unidades de processamento gráfico (GPUs) em aplicações fora do domínio gráfico. Essa tendência ao desenvolvimento de propósitos gerais com a GPU (GPGPU) foi intensificada com a produção de APIs não-gráficas, tais como a Compute Unified Device Architecture (CUDA), da NVIDIA. Com elas, estudou-se a solução na GPU de muitos problemas de processamento de sinal 2D e 3D envolvendo álgebra linear e equações diferenciais parciais, mas pouca atenção tem sido dada ao processamento de sinais 1D, que também podem exigir recursos computacionais significativos. Já havia sido demonstrado que a GPU pode ser usada para processamento de sinais em tempo-real, mas alguns processos não se adequavam bem à arquitetura da GPU. Neste trabalho, apresento uma nova técnica para implementar um filtro digital linear recursivo usando a GPU. Até onde eu sei, a solução aqui apresentada é a primeira na literatura. Uma comparação entre esta abordagem e uma implementação equivalente baseada na CPU demonstra que, quando usada em um sistema de processamento de áudio em temporeal, esta técnica permite o processamento de duas a quatro vezes mais coeficientes do que era possível anteriormente. A técnica também elimina a necessidade de processar o filtro na CPU - evitando transferências de memória adicionais entre CPU e GPU - quando se deseja usar o filtro junto a outros processos, tais como síntese de som. A recursividade estabelecida pela equação do filtro torna difícil obter uma implementação eficiente em uma arquitetura paralela como a da GPU. Já que cada amostra de saída é computada em paralelo, os valores necessários de amostras de saída anteriores não estão disponíveis no momento do cômputo. Poder-se-ia forçar a GPU a executar o filtro sequencialmente usando sincronização, mas isso seria um uso ineficiente da GPU. Este problema foi resolvido desdobrando-se a equação e "trocando-se" as dependências de amostras próximas à saída atual por outras precedentes, assim exigindo apenas o armazenamento de um certo número de amostras de saída. A equação resultante contém convoluções que então são eficientemente computadas usando a FFT. A implementação da técnica é geral e funciona para qualquer filtro recursivo linear invariante no tempo. Para demonstrar sua relevância, construímos um filtro LPC para sintetizar em tempo-real sons realísticos de colisões de objetos feitos de diferentes materiais, tais como vidro, plástico e madeira. Os sons podem ser parametrizados por material dos objetos, velocidade e ângulo das colisões. Apesar de flexível, esta abordagem usa pouca memória, exigindo apenas alguns coeficientes para representar a resposta ao impulso do filtro para cada material. Isso torna esta abordagem uma alternativa atraente frente às técnicas tradicionais baseadas em CPU que apenas realizam a reprodução de sons gravados. / Many researchers have been interested in exploring the vast computational power of recent graphics processing units (GPUs) in applications outside the graphics domain. This trend towards General-Purpose GPU (GPGPU) development has been intensified with the release of non-graphics APIs for GPU programming, such as NVIDIA's Compute Unified Device Architecture (CUDA). With them, the GPU has been widely studied for solving many 2D and 3D signal processing problems involving linear algebra and partial differential equations, but little attention has been given to 1D signal processing, which may demand significant computational resources likewise. It has been previously demonstrated that the GPU can be used for real-time signal processing, but several processes did not fit the GPU architecture well. In this work, a new technique for implementing a digital recursive linear filter using the GPU is presented. To the best of my knowledge, the solution presented here is the first in the literature. A comparison between this approach and an equivalent CPU-based implementation demonstrates that, when used in a real-time audio processing system, this technique supports processing of two to four times more coefficients than it was possible previously. The technique also eliminates the necessity of processing the filter on the CPU - avoiding additional memory transfers between CPU and GPU - when one wishes to use the filter in conjunction with other processes, such as sound synthesis. The recursivity established by the filter equation makes it difficult to obtain an efficient implementation on a parallel architecture like the GPU. Since every output sample is computed in parallel, the necessary values of previous output samples are unavailable at the time the computation takes place. One could force the GPU to execute the filter sequentially using synchronization, but this would be a very inefficient use of GPU resources. This problem is solved by unrolling the equation and "trading" dependences on samples close to the current output by other preceding ones, thus requiring only the storage of a limited number of previous output samples. The resulting equation contains convolutions which are then efficiently computed using the FFT. The proposed technique's implementation is general and works for any time-invariant recursive linear filter. To demonstrate its relevance, an LPC filter is designed to synthesize in real-time realistic sounds of collisions between objects made of different materials, such as glass, plastic, and wood. The synthesized sounds can be parameterized by the objects' materials, velocities and collision angles. Despite its flexibility, this approach uses very little memory, requiring only a few coefficients to represent the impulse response for the filter of each material. This turns this approach into an attractive alternative to traditional CPU-based techniques that use playback of pre-recorded sounds.

Muitos pesquisadores têm se interessado em explorar o vasto poder computacional das recentes unidades de processamento gráfico (GPUs) em aplicações fora do domínio gráfico. Essa tendência ao desenvolvimento de propósitos gerais com a GPU (GPGPU) foi intensificada com a produção de APIs não-gráficas, tais como a Compute Unified Device Architecture (CUDA), da NVIDIA. Com elas, estudou-se a solução na GPU de muitos problemas de processamento de sinal 2D e 3D envolvendo álgebra linear e equações diferenciais parciais, mas pouca atenção tem sido dada ao processamento de sinais 1D, que também podem exigir recursos computacionais significativos. Já havia sido demonstrado que a GPU pode ser usada para processamento de sinais em tempo-real, mas alguns processos não se adequavam bem à arquitetura da GPU. Neste trabalho, apresento uma nova técnica para implementar um filtro digital linear recursivo usando a GPU. Até onde eu sei, a solução aqui apresentada é a primeira na literatura. Uma comparação entre esta abordagem e uma implementação equivalente baseada na CPU demonstra que, quando usada em um sistema de processamento de áudio em temporeal, esta técnica permite o processamento de duas a quatro vezes mais coeficientes do que era possível anteriormente. A técnica também elimina a necessidade de processar o filtro na CPU - evitando transferências de memória adicionais entre CPU e GPU - quando se deseja usar o filtro junto a outros processos, tais como síntese de som. A recursividade estabelecida pela equação do filtro torna difícil obter uma implementação eficiente em uma arquitetura paralela como a da GPU. Já que cada amostra de saída é computada em paralelo, os valores necessários de amostras de saída anteriores não estão disponíveis no momento do cômputo. Poder-se-ia forçar a GPU a executar o filtro sequencialmente usando sincronização, mas isso seria um uso ineficiente da GPU. Este problema foi resolvido desdobrando-se a equação e "trocando-se" as dependências de amostras próximas à saída atual por outras precedentes, assim exigindo apenas o armazenamento de um certo número de amostras de saída. A equação resultante contém convoluções que então são eficientemente computadas usando a FFT. A implementação da técnica é geral e funciona para qualquer filtro recursivo linear invariante no tempo. Para demonstrar sua relevância, construímos um filtro LPC para sintetizar em tempo-real sons realísticos de colisões de objetos feitos de diferentes materiais, tais como vidro, plástico e madeira. Os sons podem ser parametrizados por material dos objetos, velocidade e ângulo das colisões. Apesar de flexível, esta abordagem usa pouca memória, exigindo apenas alguns coeficientes para representar a resposta ao impulso do filtro para cada material. Isso torna esta abordagem uma alternativa atraente frente às técnicas tradicionais baseadas em CPU que apenas realizam a reprodução de sons gravados. / Many researchers have been interested in exploring the vast computational power of recent graphics processing units (GPUs) in applications outside the graphics domain. This trend towards General-Purpose GPU (GPGPU) development has been intensified with the release of non-graphics APIs for GPU programming, such as NVIDIA's Compute Unified Device Architecture (CUDA). With them, the GPU has been widely studied for solving many 2D and 3D signal processing problems involving linear algebra and partial differential equations, but little attention has been given to 1D signal processing, which may demand significant computational resources likewise. It has been previously demonstrated that the GPU can be used for real-time signal processing, but several processes did not fit the GPU architecture well. In this work, a new technique for implementing a digital recursive linear filter using the GPU is presented. To the best of my knowledge, the solution presented here is the first in the literature. A comparison between this approach and an equivalent CPU-based implementation demonstrates that, when used in a real-time audio processing system, this technique supports processing of two to four times more coefficients than it was possible previously. The technique also eliminates the necessity of processing the filter on the CPU - avoiding additional memory transfers between CPU and GPU - when one wishes to use the filter in conjunction with other processes, such as sound synthesis. The recursivity established by the filter equation makes it difficult to obtain an efficient implementation on a parallel architecture like the GPU. Since every output sample is computed in parallel, the necessary values of previous output samples are unavailable at the time the computation takes place. One could force the GPU to execute the filter sequentially using synchronization, but this would be a very inefficient use of GPU resources. This problem is solved by unrolling the equation and "trading" dependences on samples close to the current output by other preceding ones, thus requiring only the storage of a limited number of previous output samples. The resulting equation contains convolutions which are then efficiently computed using the FFT. The proposed technique's implementation is general and works for any time-invariant recursive linear filter. To demonstrate its relevance, an LPC filter is designed to synthesize in real-time realistic sounds of collisions between objects made of different materials, such as glass, plastic, and wood. The synthesized sounds can be parameterized by the objects' materials, velocities and collision angles. Despite its flexibility, this approach uses very little memory, requiring only a few coefficients to represent the impulse response for the filter of each material. This turns this approach into an attractive alternative to traditional CPU-based techniques that use playback of pre-recorded sounds.

Muitos pesquisadores têm se interessado em explorar o vasto poder computacional das recentes unidades de processamento gráfico (GPUs) em aplicações fora do domínio gráfico. Essa tendência ao desenvolvimento de propósitos gerais com a GPU (GPGPU) foi intensificada com a produção de APIs não-gráficas, tais como a Compute Unified Device Architecture (CUDA), da NVIDIA. Com elas, estudou-se a solução na GPU de muitos problemas de processamento de sinal 2D e 3D envolvendo álgebra linear e equações diferenciais parciais, mas pouca atenção tem sido dada ao processamento de sinais 1D, que também podem exigir recursos computacionais significativos. Já havia sido demonstrado que a GPU pode ser usada para processamento de sinais em tempo-real, mas alguns processos não se adequavam bem à arquitetura da GPU. Neste trabalho, apresento uma nova técnica para implementar um filtro digital linear recursivo usando a GPU. Até onde eu sei, a solução aqui apresentada é a primeira na literatura. Uma comparação entre esta abordagem e uma implementação equivalente baseada na CPU demonstra que, quando usada em um sistema de processamento de áudio em temporeal, esta técnica permite o processamento de duas a quatro vezes mais coeficientes do que era possível anteriormente. A técnica também elimina a necessidade de processar o filtro na CPU - evitando transferências de memória adicionais entre CPU e GPU - quando se deseja usar o filtro junto a outros processos, tais como síntese de som. A recursividade estabelecida pela equação do filtro torna difícil obter uma implementação eficiente em uma arquitetura paralela como a da GPU. Já que cada amostra de saída é computada em paralelo, os valores necessários de amostras de saída anteriores não estão disponíveis no momento do cômputo. Poder-se-ia forçar a GPU a executar o filtro sequencialmente usando sincronização, mas isso seria um uso ineficiente da GPU. Este problema foi resolvido desdobrando-se a equação e "trocando-se" as dependências de amostras próximas à saída atual por outras precedentes, assim exigindo apenas o armazenamento de um certo número de amostras de saída. A equação resultante contém convoluções que então são eficientemente computadas usando a FFT. A implementação da técnica é geral e funciona para qualquer filtro recursivo linear invariante no tempo. Para demonstrar sua relevância, construímos um filtro LPC para sintetizar em tempo-real sons realísticos de colisões de objetos feitos de diferentes materiais, tais como vidro, plástico e madeira. Os sons podem ser parametrizados por material dos objetos, velocidade e ângulo das colisões. Apesar de flexível, esta abordagem usa pouca memória, exigindo apenas alguns coeficientes para representar a resposta ao impulso do filtro para cada material. Isso torna esta abordagem uma alternativa atraente frente às técnicas tradicionais baseadas em CPU que apenas realizam a reprodução de sons gravados. / Many researchers have been interested in exploring the vast computational power of recent graphics processing units (GPUs) in applications outside the graphics domain. This trend towards General-Purpose GPU (GPGPU) development has been intensified with the release of non-graphics APIs for GPU programming, such as NVIDIA's Compute Unified Device Architecture (CUDA). With them, the GPU has been widely studied for solving many 2D and 3D signal processing problems involving linear algebra and partial differential equations, but little attention has been given to 1D signal processing, which may demand significant computational resources likewise. It has been previously demonstrated that the GPU can be used for real-time signal processing, but several processes did not fit the GPU architecture well. In this work, a new technique for implementing a digital recursive linear filter using the GPU is presented. To the best of my knowledge, the solution presented here is the first in the literature. A comparison between this approach and an equivalent CPU-based implementation demonstrates that, when used in a real-time audio processing system, this technique supports processing of two to four times more coefficients than it was possible previously. The technique also eliminates the necessity of processing the filter on the CPU - avoiding additional memory transfers between CPU and GPU - when one wishes to use the filter in conjunction with other processes, such as sound synthesis. The recursivity established by the filter equation makes it difficult to obtain an efficient implementation on a parallel architecture like the GPU. Since every output sample is computed in parallel, the necessary values of previous output samples are unavailable at the time the computation takes place. One could force the GPU to execute the filter sequentially using synchronization, but this would be a very inefficient use of GPU resources. This problem is solved by unrolling the equation and "trading" dependences on samples close to the current output by other preceding ones, thus requiring only the storage of a limited number of previous output samples. The resulting equation contains convolutions which are then efficiently computed using the FFT. The proposed technique's implementation is general and works for any time-invariant recursive linear filter. To demonstrate its relevance, an LPC filter is designed to synthesize in real-time realistic sounds of collisions between objects made of different materials, such as glass, plastic, and wood. The synthesized sounds can be parameterized by the objects' materials, velocities and collision angles. Despite its flexibility, this approach uses very little memory, requiring only a few coefficients to represent the impulse response for the filter of each material. This turns this approach into an attractive alternative to traditional CPU-based techniques that use playback of pre-recorded sounds.

This thesis covers the development of a series of new methods and the application of adaptive filter theory which are combined to produce a generalised adaptive filter system which may be used to perform such tasks as pattern recognition. Firstly, the relevant background adaptive filter theory is discussed in Chapter 1 and methods and results which are important to the rest of the thesis are derived or referenced. Chapter 2 of this thesis covers the development of a new adaptive algorithm which is designed to give faster convergence than the LMS algorithm but unlike the Recursive Least Squares family of algorithms it does not require storage of a matrix with n2 elements, where n is the number of filter taps. In Chapter 3 a new extension of the LMS adaptive notch filter is derived and applied which gives an adaptive notch filter the ability to lock and track signals of varying pitch without sacrificing notch depth. This application of the LMS filter is of interest as it demonstrates a time varying filter solution to a stationary problem. The LMS filter is next extended to the multidimensional case which allows the application of LMS filters to image processing. The multidimensional filter is then applied to the problem of image registration and this new application of the LMS filter is shown to have significant advantages over current image registration methods. A consideration of the multidimensional LMS filter as a template matcher and pattern recogniser is given. In Chapter 5 a brief review of statistical pattern recognition is given, and in Chapter 6 a review of relevant connectionist models. In Chapter 7 the generalised adaptive filter is derived. This is an adaptive filter with the ability to model non-linear input-output relationships. The Volterra functional analysis of non-linear systems is given and this is combined with adaptive filter methods to give a generalised non-linear adaptive digital filter. This filter is then considered as a linear adaptive filter operating in a non-linearly extended vector space. This new filter is shown to have desirable properties as a pattern recognition system. The performance and properties of the new filter is compared with current connectionist models and results demonstrated in Chapter 8. In Chapter 9 further mathematical analysis of the networks leads to suggested methods to greatly reduce network complexity for a given problem by choosing suitable pattern classification indices and allowing it to define its own internal structure. In Chapter 10 robustness of the network to imperfections in its implementation is considered. Chapter 11 finishes the thesis with some conclusions and suggestions for future work.