Browsing by Subject "wavelets"
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Item Bayesian classification and survival analysis with curve predictors(2009-05-15) Wang, XiaohuiWe propose classification models for binary and multicategory data where the predictor is a random function. The functional predictor could be irregularly and sparsely sampled or characterized by high dimension and sharp localized changes. In the former case, we employ Bayesian modeling utilizing flexible spline basis which is widely used for functional regression. In the latter case, we use Bayesian modeling with wavelet basis functions which have nice approximation properties over a large class of functional spaces and can accommodate varieties of functional forms observed in real life applications. We develop an unified hierarchical model which accommodates both the adaptive spline or wavelet based function estimation model as well as the logistic classification model. These two models are coupled together to borrow strengths from each other in this unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible. We compare the performance of the proposed models with the naive models as well as existing alternatives by analyzing simulated as well as real data. We also propose a Bayesian unified hierarchical model based on a proportional hazards model and generalized linear model for survival analysis with irregular longitudinal covariates. This relatively simple joint model has two advantages. One is that using spline basis simplifies the parameterizations while a flexible non-linear pattern of the function is captured. The other is that joint modeling framework allows sharing of the information between the regression of functional predictors and proportional hazards modeling of survival data to improve the efficiency of estimation. The novel method can be used not only for one functional predictor case, but also for multiple functional predictors case. Our methods are applied to analyze real data sets and compared with a parameterized regression method.Item Improving Filtering for Computer Graphics(2014-04-30) Manson, JosiahWhen drawing images onto a computer screen, the information in the scene is typically more detailed than can be displayed. Most objects, however, will not be close to the camera, so details have to be filtered out, or anti-aliased, when the objects are drawn on the screen. I describe new methods for filtering images and shapes with high fidelity while using computational resources as efficiently as possible. Vector graphics are everywhere, from drawing 3D polygons to 2D text and maps for navigation software. Because of its numerous applications, having a fast, high-quality rasterizer is important. I developed a method for analytically rasterizing shapes using wavelets. This approach allows me to produce accurate 2D rasterizations of images and 3D voxelizations of objects, which is the first step in 3D printing. I later improved my method to handle more filters. The resulting algorithm creates higher-quality images than commercial software such as Adobe Acrobat and is several times faster than the most highly optimized commercial products. The quality of texture filtering also has a dramatic impact on the quality of a rendered image. Textures are images that are applied to 3D surfaces, which typically cannot be mapped to the 2D space of an image without introducing distortions. For situations in which it is impossible to change the rendering pipeline, I developed a method for precomputing image filters over 3D surfaces. If I can also change the pipeline, I show that it is possible to improve the quality of texture sampling significantly in real-time rendering while using the same memory bandwidth as used in traditional methods.Item Modeling the effect of land cover land use change on estuarine environmental flows(2009-05-15) Sahoo, DebabrataEnvironmental flows are important to maintain the ecological integrity of the estuary. In a watershed, it is influenced by land use land cover (LULC) change, climate variability, and water regulations. San Antonio, Texas, the 8th largest city in the US, is likely to affect environmental flows to the San Antonio Bay/Guadalupe Estuary, due to rapid urbanization. Time series analysis was conducted at several stream gauging stations to assess trends in hydrologic variables. A bootstrapping method was employed to estimate the critical value for global significance. Results suggested a greater number of trends are observed than are expected to occur by chance. Stream gauging stations present in lower half of the watershed experienced increasing trend, whereas upper half experienced decreasing trends. A similar spatial pattern was not observed for rainfall. Winter season observed maximum number of trends. Wavelet analysis on hydrologic variables, suggested presence of multi-scale temporal variability; dominant frequencies in 10 to 15 year scale was observed in some of the hydrologic variables, with a decadal cycle. Dominant frequencies were also observed in 17 to 23 year scale with repeatability in 20 to 30 years. It is therefore important to understand various ecological processes that are dominant in this scale and quantify possible linkages among them. Genetic algorithm (GA) was used for calibration of the Hydrologic Simulation Program in FORTRAN (HSPF) model. Although, GA is computationally demanding, it is better than manual calibration. Parameter values obtained for the calibrated model had physical representation and were well within the ranges suggested in the literature. Information from LANDSAT images for the years 1987, 1999, and 2003 were introduced to HSPF to quantify the impact of LULC change on environmental flows. Modeling studies indicated, with increase in impervious surface, peak flows increased over the years. Wavelet analysis pointed, that urbanization also impacted storage. Modeling studies quantified, on average about 50% of variability in freshwater inflows could be attributed to variation in precipitation, and approximately 10% of variation in freshwater inflows could be attributed to LULC change. This study will help ecologist, engineers, scientist, and politicians in policy making pertinent to water resources management.Item Reservoir characterization using wavelet transforms(Texas A&M University, 2004-09-30) Rivera Vega, NestorAutomated detection of geological boundaries and determination of cyclic events controlling deposition can facilitate stratigraphic analysis and reservoir characterization. This study applies the wavelet transformation, a recent advance in signal analysis techniques, to interpret cyclicity, determine its controlling factors, and detect zone boundaries. We tested the cyclostratigraphic assessments using well log and core data from a well in a fluvio-eolian sequence in the Ormskirk Sandstone, Irish Sea. The boundary detection technique was tested using log data from 10 wells in the Apiay field, Colombia. We processed the wavelet coefficients for each zone of the Ormskirk Formation and determined the wavelengths of the strongest cyclicities. Comparing these periodicities with Milankovitch cycles, we found a strong correspondence of the two. This suggests that climate exercised an important control on depositional cyclicity, as had been concluded in previous studies of the Ormskirk Sandstone. The wavelet coefficients from the log data in the Apiay field were combined to form features. These vectors were used in conjunction with pattern recognition techniques to perform detection in 7 boundaries. For the upper two units, the boundary was detected within 10 feet of their actual depth, in 90% of the wells. The mean detection performance in the Apiay field is 50%. We compared our method with other traditional techniques which do not focus on selecting optimal features for boundary identification. Those methods resulted in detection performances of 40% for the uppermost boundary, which lag behind the 90% performance of our method. Automated determination of geologic boundaries will expedite studies, and knowledge of the controlling deposition factors will enhance stratigraphic and reservoir characterization models. We expect that automated boundary detection and cyclicity analysis will prove to be valuable and time-saving methods for establishing correlations and their uncertainties in many types of oil and gas reservoirs, thus facilitating reservoir exploration and management.Item Some applications of wavelets to time series data(2009-05-15) Jeong, Jae SikThe objective of this dissertation is to develop a suitable statistical methodology for parameter estimation in long memory process. Time series data with complex covariance structure are shown up in various fields such as finance, computer network, and econometrics. Many researchers suggested the various methodologies defined in different domains: frequency domain and time domain. However, many traditional statistical methods are not working well in complicated case, for example, nonstationary process. The development of the robust methodologies against nonstationarity is the main focus of my dissertation. We suggest a wavelet-based Bayesian method which shares good properties coming from both wavelet-based method and Bayesian approach. To check the robustness of the method, we consider ARFIMA(0, d, 0) with linear trend. Also, we compare the result of the method with that of several existing methods, which are defined in different domains, i.e. time domain estimators, frequency domain estimators. Also, we apply the method to functional magnetic resonance imaging (fMRI) data to find some connection between brain activity and long memory parameter. Another objective of this dissertation is to develop a wavelet-based denoising technique when there is heterogeneous variance noise in high throughput data, especially protein mass spectrometry data. Since denoising technique pretty much depends on threshold value, it is very important to get a proper threshold value which involves estimate of standard deviation. To this end, we detect variance change point first and get suitable threshold values in each segment. After that, we apply local wavelet thresholding to each segment, respectively. For comparison, we consider several existing global thresholding methods.