Smooth Affine Shear Tight Frames with 2-Layer Structure and Their Applications 


Student thesis: Doctoral Thesis

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Award date22 Aug 2018


In this thesis, we characterize and construct a new multiscale directional representation system -- an affine shear tight frame with 2-layer structure -- ASF-2, in short, and its associated digital affine shear filter bank with 2-layer structure -- DAS-2. Their efficiency are demonstrated by various experiments including image/video denoising/inpainting, surface denoising and texture classification. The content of this thesis consists of five chapters.

The first chapter recounts the motivation of our work by classical shearlets which has single layer structure and tensor product directional filter banks TP-CTF6 or TP-CTF6 which shows a 2-layer structure. In Chapter 2, the general classical MRA-based frame theory developed for painless construction of tight wavelet frames is reviewed and it plays a fundamental tool in our construction. The first two sections in Chapter 3 are dedicated to review main ideas of the theory of classical shearlets and that of tensor product directional filter banks TP-CTF6 or TP-CTF6. Then the rest part of this chapter gives a detailed construction and characterization of our proposed tight wavelet frame ASF-2 together with its associated filter bank DAS-2. Chapter 4 shows a series of experiments to demonstrate the performance of the new DAS-2 filter bank. The last chapter describes some potential future direction on design and construction of multiscale directional representation systems.