Adaptive Wavelet Transforms Via Lifting
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Adaptive Wavelet Transforms Via Lifting
Wavelet transforms have proven very useful for a variety of signal and image processing tasks. The wedgelet transform also shows promise for certain edge-dominated images. However, in many applications we desire to introduce adaptivity and nonlinearities into the transforms. These are powerful extensions, but difficult to control within the wavelet framework. The lifting scheme provides a new, spatial intuition into the wavelet transform that simplifies the introduction of adaptivity. In this thesis, we develop several new adaptive wavelet transforms and adaptive multiresolution wedgelet transforms. The lifting construction permits control over the multiresolution properties of these transforms despite the adaptivity. We demonstrate the power of our new adaptive lifted transforms with successful applications to signal denoising and compression problems.
Adaptive Wavelet Transforms Via Lifting
Wavelet transforms have proven very useful for a variety of signal and image processing tasks. The wedgelet transform also shows promise for certain edge-dominated images. However, in many applications we desire to introduce adaptivity and nonlinearities into the transforms. These are powerful extensions, but difficult to control within the wavelet framework. The lifting scheme provides a new, spatial intuition into the wavelet transform that simplifies the introduction of adaptivity. In this thesis, we develop several new adaptive wavelet transforms and adaptive multiresolution wedgelet transforms. The lifting construction permits control over the multiresolution properties of these transforms despite the adaptivity. We demonstrate the power of our new adaptive lifted transforms with successful applications to signal denoising and compression problems.
Theory of Wavelets: From Design Principles to Applications
The recent advancements in digital image, machine vision, and artificial intelligence have greatly propelled the field of wavelet-based signal processing. The primary aim of this book is to equip readers, regardless of their familiarity with signal processing, with a solid foundation in the subject. The book delves into the fundamental concepts, enabling readers to gain a comprehensive understanding and eventually apply their knowledge to practical scenarios. It offers a thorough explanation of the underlying principles and showcases various wavelet-based applications. To illustrate key concepts and methodologies, comprehensive solutions and meticulous analysis of numerical data are presented. This book serves as an essential text for graduate and post-graduate students, as well as a valuable reference for wavelet design experts embarking on their journey in the field.