CONSTRUCTION OF SYMMETRIC TIGHT WAVELET FRAMES AND THEIR APPLICATIONS
Myungjin Choi, Hong Oh Kim · 한국산업응용수학회 학술대회 논문집 · 2006
Orthogonal wavelets and their various generalizations have been extensively studied in the literature and they have been successfully applied to many applications. Without introducing other types of wavelets in this work, we are particularly focused on symmetric tight wavelet frames (STWFs), which are derived from a refinable function. The notion of tight wavelet frames could be considered as a natural generalization of orthonormal wavelets if redundancy is introduced into the wavelet system. By allowing redundancy, we gain the necessary flexibility to achieve such properties as symmetry and, more importantly, the short support and high vanishing moments of compactly supported wavelets. In addition, redundancy allows for the approximate shift invariance behavior caused by the dense time-scale plane. In this work, we present the construction of STWFs with the desired properties and then consider some examples of how we can apply STWFs to the area of image processing, particularly image denoising, image enhancement, and image fusion.