WAVELET PACKET FRAME-BASED IMAGE RESTORATION MODELS AND THEIR ASYMPTOTIC ANALYSIS

Abstract

In my thesis, a novel class of wavelet packet frame (WPF)-based image restoration models has been studied, which generalizes a variety of existing models, including the balanced model and a notable inf-convolution model. For this purpose, the theory of wavelet packet frames, which refines that of wavelet frames in time-frequency analysis, has been reviewed and adequately developed. Simultaneously, the method of asymptotic analysis, a theoretical framework that validates a comprehensive and heuristic investigation of a discrete model together with its continual counterpart, has been applied to establish the connection between a classical setting of the WPF model (the generalized analysis WPF model) and a total generalized variational (or TGV) model, which in particular provides an asymptotic characterization of the former's minimizers at rising resolution levels. Image restoration experiments have been conducted based on existing and newly designed algorithms.