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Author: Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
We are developing a general theory for multi scale signal and image modeling, processing, and analysis that matched to singularity-rich data, such as transients and images with edges. Using a linguistic analogy, our model can be interpreted as grammars that constrain the wavelet vocabulary. Our investigation focuses on probabilistic graph models (tree-based hidden Markov models) that can accurately, realistically, and efficiently represent singularity structure in the wavelet domain. Grammar design is being guided by a detailed study of the final structure of singularities using Besov spaces and multifractal analysis.
Author: Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
We are developing a general theory for multi scale signal and image modeling, processing, and analysis that matched to singularity-rich data, such as transients and images with edges. Using a linguistic analogy, our model can be interpreted as grammars that constrain the wavelet vocabulary. Our investigation focuses on probabilistic graph models (tree-based hidden Markov models) that can accurately, realistically, and efficiently represent singularity structure in the wavelet domain. Grammar design is being guided by a detailed study of the final structure of singularities using Besov spaces and multifractal analysis.
Author: Xiaoping Shen Publisher: Springer Science & Business Media ISBN: 1461441455 Category : Technology & Engineering Languages : en Pages : 388
Book Description
Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.
Author: Paul Fieguth Publisher: Springer Science & Business Media ISBN: 1441972943 Category : Mathematics Languages : en Pages : 465
Book Description
Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something—an artery, a road, a DNA marker, an oil spill—from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over a two or higher dimensional space, and to which standard image-processing algorithms may not apply. There are many important data analysis methods developed in this text for such statistical image problems. Examples abound throughout remote sensing (satellite data mapping, data assimilation, climate-change studies, land use), medical imaging (organ segmentation, anomaly detection), computer vision (image classification, segmentation), and other 2D/3D problems (biological imaging, porous media). The goal, then, of this text is to address methods for solving multidimensional statistical problems. The text strikes a balance between mathematics and theory on the one hand, versus applications and algorithms on the other, by deliberately developing the basic theory (Part I), the mathematical modeling (Part II), and the algorithmic and numerical methods (Part III) of solving a given problem. The particular emphases of the book include inverse problems, multidimensional modeling, random fields, and hierarchical methods.
Author: Marco A.R. Ferreira Publisher: Springer Science & Business Media ISBN: 0387708987 Category : Mathematics Languages : en Pages : 243
Book Description
This highly useful book contains methodology for the analysis of data that arise from multiscale processes. It brings together a number of recent developments and makes them accessible to a wider audience. Taking a Bayesian approach allows for full accounting of uncertainty, and also addresses the delicate issue of uncertainty at multiple scales. These methods can handle different amounts of prior knowledge at different scales, as often occurs in practice.
Author: Jieqian He Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 160
Book Description
Wavelet analysis and deep learning are two popular fields for signal processing. The scattering transform from wavelet analysis is a recently proposed mathematical model for convolution neural networks. Signals with repeated patterns can be analyzed using the statistics from such models. Specifically, signals from certain classes can be recovered from related statistics. We first focus on recovering 1D deterministic dirac signals from multiscale statistics. We prove a dirac signal can be recovered from multiscale statistics up to a translation and reflection. Then we switch to a stochastic version, modeled using Poisson point processes, and prove wavelet statistics at small scales capture the intensity parameter of Poisson point processes. We also design a scattering generative adversarial network (GAN) to generate new Poisson point samples from statistics of multiple given samples. Next we consider texture images. We successfully synthesize new textures given one sample from the texture class through multiscale, multilayer wavelet models. Finally, we analyze and prove why the multiscale multilayer model is essential for signal recovery, especially natural texture images.
Author: Anthony O' Hagan Publisher: OUP Oxford ISBN: 0191613894 Category : Mathematics Languages : en Pages : 924
Book Description
Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
Author: Kenneth C. Chou Publisher: ISBN: Category : Languages : en Pages : 11
Book Description
Signal processing for condition based maintenance and equipment monitoring has focused in recent years on non-stationary signal analysis using time-frequency representations of the signal. These representations are used to identify non-stationary events in the signal that indicate some change in the state of a structure or a machine. It is important to be able to reliably detect such changes in real time to do necessary preventive maintenance and also to minimize unnecessary maintenance. While transformations such as the Wigner-Ville, Gabor, and wavelet transforms are useful in highlighting time-frequency features of the signal, the application of such transforms to the monitoring problem requires additional for making decisions concerning the condition of the object being monitored. In particular, the interpretation of the transform coefficients in terms of physical events is essential to making such decisions. We develop a methodology for identifying the physical state of the object based on statistical models of the signals, which could comprise, for example, multiple outputs from devices such as accelerometers, strain sensors and acoustic emission sensors. Classification of machine states based on monitoring signals is performed by comparing likelihood scores for each machine state. We present examples of applying our system to various data, including damped sinusoids and noisy chirps, as a way of illustrating system performance for the case of transient monitoring signals. We compare our system to one which is trained using a DFT-based (non-time-frequency-based) representation (in particular, LPC coefficients) and show that our system exhibits both superior performance as well as greater robustness to noise in the signals.
Author: Publisher: ISBN: Category : Languages : en Pages : 28
Book Description
This project pursued a general theory for complex-valued multiscale signal and image modeling, processing, and analysis that is matched to singularity-rich data. Higher-dimensional signals that feature geometric manifold structures were of particular interest in developing theory and a practical toolset for analysis and processing. We pursued a three-pronged approach in creating new multiscale transforms, new geometric statistical models, and new manifold-based signal representations. The results of our research include (1) the Dual Tree Quaternion Wavelet, an efficient transform and analysis tool that features near shift invariance and linear computational complexity; (2) a geometric hidden Markov tree wavelet model, which accounts for geometric regularity by capturing the dependencies between complex wavelet coefficients along a contour; and (3) surflet representations of signal discontinuities with near optimal rate-distortion performance. These new tools have led to significant performance gains immediately applicable to a number of important Navy-relevant applications, including target detection and classification, image segmentation and fusion, and computer network traffic modeling.
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Author: Xiaoping Shen
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Author: Paul Fieguth
Author: Michael Klaus Schneider
Author: Marco A.R. Ferreira
Author: Jieqian He
Author: Anthony O' Hagan
Author: Kenneth C. Chou
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