Este trabalho analisa a viabilidade de implementação de um sistema de compressão de vídeo em FPGAs com restrições de área e de recursos de roteamento, de modo a estudar as possibilidades oferecidas por pequenas áreas de lógica reconfigurável associadas a processadores clássicos. A técnica de eliminação de redundância espacial adotada é a Transformada Wavelet (WT), ao invés da já bastante explorada Transformada Cosseno (DCT). A arquitetura selecionada para efetuar a DWT é implementada no FPGA Xilinx XC6200, que apresenta características muito interessantes de reconfiguração rápida e dinâmica. Também foi desenvolvido um modelo estatístico dos erros de quantização associados à implementação da Transformada Waveletem aritmética de ponto fixo, auxiliando uma implementação em hardware mais eficiente em termos de área e desempenho. Algumas arquiteturas alternativas para a DWT são implementadas, para avaliação dos méritos de cada uma delas. Para permitir esta implementação, uma biblioteca de funções para processamento de sinais otimizada para o FPGA XC6200 também foi desenvolvida. Os resultados mostram que um sistema completo de compressão, utilizando os filtros propostos por Daubechies pode ser implementado utilizando o equivalente a 2500 portas lógicas e atinge taxas de compressão de aproximadamente 8 vezes sem perda significativa de qualidade em imagens monocromáticas de 256x256 pixels a 30 quadros por segundo / The purpose of this work is to study the problems associated with the implementation of a image compression system implemented with fine-grained FPGAs with scarce routing resources. The study intends to explore possibilities offered by small areas of reconfigurable logic coupled to classical processors. The image compression technique adopted was Discrete Wavelet Transform (DWT), instead the well-known Discrete Cosine Transform. The architecture was built in a Xilinx FPGA, the XC6200, a very interesting device due to its dynamic reconfigurable features. It was also developed a study about quantization errors in DWT processed with fixed point arithmetic. Some other DWT architectures are presented and the advantages are discussed. The implementation of these architectures led to the development of signal processing libraries optimized to XC6200. The implementation was made with only 2500 gates and showed that is possible to reach video rates. Frame sizes are 256x256 with 256 gray levels, and the compression rate is about 8 times

No description available.

Measurements of vibrations, such as sound hitting an object or running a motor, are widely used in industry and research. Traditional methods need either direct contact with the object or a laser vibrometer. Although computer vision methods have been applied to solve this problem, high speed cameras are usually preferred. This study employs a consumer level rolling shutter camera for extracting main frequency components of small vibrations. A rolling shutter camera exposes continuously over time on the vertical direction of the sensor, and produces images with shifted rows of objects. We utilize the rolling shutter effect to boost our capability to extract vibration frequencies higher than the frame rate. Assuming the vibration amplitude of the target results in a horizontal fronto-parallel component in the image, we compute the displacement of each row from a reference frame by our novel phase matching approach in the complex-valued Shearlet transform domain. So far the only way to process rolling shutter video for vibration extraction is with the Steerable Pyramid in a motion magnification framework. However, the Shearlet transform is well localized in scale, location and orientation, and hence better suited to vibration extraction than the Steerable Pyramid used in the high speed video approach. Using our rolling shutter approach, we manage to recover signals from 75Hz to 500Hz from videos of 30fps. We test our method by controlled experiments with a loudspeaker. We play sounds with certain frequency components and take videos of the loudspeaker's surface. Our approach recovers chirp signals as well as single frequency signals from rolling shutter videos. We also test with music and speech. Both experiments produce identifiable recovered audio.

Este trabalho analisa a viabilidade de implementação de um sistema de compressão de vídeo em FPGAs com restrições de área e de recursos de roteamento, de modo a estudar as possibilidades oferecidas por pequenas áreas de lógica reconfigurável associadas a processadores clássicos. A técnica de eliminação de redundância espacial adotada é a Transformada Wavelet (WT), ao invés da já bastante explorada Transformada Cosseno (DCT). A arquitetura selecionada para efetuar a DWT é implementada no FPGA Xilinx XC6200, que apresenta características muito interessantes de reconfiguração rápida e dinâmica. Também foi desenvolvido um modelo estatístico dos erros de quantização associados à implementação da Transformada Waveletem aritmética de ponto fixo, auxiliando uma implementação em hardware mais eficiente em termos de área e desempenho. Algumas arquiteturas alternativas para a DWT são implementadas, para avaliação dos méritos de cada uma delas. Para permitir esta implementação, uma biblioteca de funções para processamento de sinais otimizada para o FPGA XC6200 também foi desenvolvida. Os resultados mostram que um sistema completo de compressão, utilizando os filtros propostos por Daubechies pode ser implementado utilizando o equivalente a 2500 portas lógicas e atinge taxas de compressão de aproximadamente 8 vezes sem perda significativa de qualidade em imagens monocromáticas de 256x256 pixels a 30 quadros por segundo / The purpose of this work is to study the problems associated with the implementation of a image compression system implemented with fine-grained FPGAs with scarce routing resources. The study intends to explore possibilities offered by small areas of reconfigurable logic coupled to classical processors. The image compression technique adopted was Discrete Wavelet Transform (DWT), instead the well-known Discrete Cosine Transform. The architecture was built in a Xilinx FPGA, the XC6200, a very interesting device due to its dynamic reconfigurable features. It was also developed a study about quantization errors in DWT processed with fixed point arithmetic. Some other DWT architectures are presented and the advantages are discussed. The implementation of these architectures led to the development of signal processing libraries optimized to XC6200. The implementation was made with only 2500 gates and showed that is possible to reach video rates. Frame sizes are 256x256 with 256 gray levels, and the compression rate is about 8 times

Signals on hierarchical trees can be viewed as a generalization of discrete signals of length 2^N. In this work, we extend the classic discrete Haar wavelets to a Haar-like wavelet basis that works for signals on hierarchical trees. We first construct a specific wavelet basis and give its inverse and normalized transform matrices. As analogue to the classic case, operators and wavelet generating functions are constructed for the tree structure. This leads to the definition of multiresolution analysis on a hierarchical tree. We prove the previously selected wavelet basis is an orthogonal multiresolution. Classification of all possible wavelet basis that generate an orthogonal multiresolution is then given. In attempt to find more efficient encoding and decoding algorithms, we construct a second wavelet basis and show that it is also an orthogonal multiresolution. The encoding and decoding algorithms are given and their time complexity are analyzed. In order to link change of tree structure and encoded signal, we define weighted hierarchical tree, tree cut and extension. It is then shown that a simply relation can be established without the need for global change of the transform matrix. Finally, we apply thresholding to the transform and give an upper bound of error.

When a shock interacts with a bubble having a different density than the environment or medium, the interaction causes compression and deformation of the bubble and generation of a vortex pair. Later, secondary vortices appear causing enhanced mixing. The enhanced mixing induced by the shock bubble interactions is particularly of interest in supersonic combustion and detonation. The Wavelet Adaptive Multi-resolution Representation (WAMR) method is particularly suitable for challenging continuum physics problems like shock bubble interaction, which has strong multi-scale character. This method provides an efficient strategy to create a dynamically adaptive spatial grid and to obtain a verified solution. Since the wavelet amplitude provides a first-hand estimate of the local error at each point, the method is able to efficiently capture a wide spectrum of spatial scales by dynamically changing the adaptive grid. Highly resolved computations are done only in the regions where abrupt transition occurs. In this work a detailed investigation of Shock Bubble Interaction (SBI) is carried out using shocks having Mach numbers from 1.2 to 3 for helium, nitrogen and krypton bubbles. Simulations carried out using WAMR method were used to analyze the effects of Mach number and density contrast on the shape, location and velocity of the bubble as well as vorticity and pressure in the flow field.

The subject of my thesis is a design of the methods optimizing, the acquisition of MR signals when small objects measure. The thesis is divided into several parts in order to give a deeper knowledge of the problem. The first part focuses on the theory associated with NMR (Nuclear Magnetic Resonance) and SNR (signal-to-noise ratio). The practical verification of the theory follows. The conclusion of this work is focused on MR images filtering by use of wavelet transform to suppress a noise in the image. The method optimization of MR acquisition parameters for the measurement of small objects is then distributed to the entire work.

In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.

Nowadays, still images are used everywhere in the digital world. The shortages of storage capacity and transmission bandwidth make efficient compression solutions essential. A revolutionary mathematics tool, wavelet transform, has already shown its power in image processing. Minimage, the major topic of this paper, is an application that compresses still images by wavelets. Minimage is used to compress grayscale images and true color images. It implements the wavelet transform to code standard BMP image files to LET wavelet image files, which is defined in Minimage. The code is written in C++ on the Microsoft Windows NT platform. This paper illustrates the design and implementation details in MinImage according to the image compression stages. First, the preprocessor generates the wavelet transform blocks. Second, the basic wavelet decomposition is applied to transform the image data to the wavelet coefficients. The discrete wavelet transforms are the kernel component of MinImage and are discussed in detail. The different wavelet transforms can be plugged in to extend the functionality of MinImage. The third step is the quantization. The standard scalar quantization algorithm and the optimized quantization algorithm, as well as the dequantization, are described. The last part of MinImage is the entropy-coding schema. The reordering of the coefficients based on the Peano Curve and the different entropy coding methods are discussed. This paper also gives the specification of the wavelet compression parameters adjusted by the end user. The interface, parameter specification, and analysis of MinImage are shown in the final appendix.

Since the cost of petroleum fluctuates widely, it is advisable to optimize extraction of oil and other hydrocarbon products form existing oil reserves. Because of the costs involved in recovering oil from a reservoir, predicting reservoir performance can be a useful tool for determining whether continued extraction might be profitable. This can be done using computer simulations of the physical processes involved such as pressure/head, fluid velocities, and so forth. Fluid flow within a reservoir occurs at a very small scale relative to the size of the reservoir. This size difference makes performing simulations at the physically appropriate scale unfeasible. Homogenization is a technique used in reservoir simulation to upscale small scale dependent behavior, such as a permeability tensor, to make simulation feasible. To calculate a homogenized permeability tensor, the solution to a system of uncoupled elliptic partial differential equations must be found repeatedly throughout the reservoir. Generally, the solution to the system of differential equations is approximated numerically using finite element or finite difference methods. We explore using wavelets as a means of characterizing homogenization in reservoir simulations in the search for fast algorithms for computing equivalent tensors. In addition to the analogy developed between homogenization and wavelets, proofs of convergence results from homogenization within the wavelet characterization are considered.