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Several studies on the frame wavelet

Author: ZhengLiE
Tutor: LiWanShe
School: Shaanxi Normal University
Course: Applied Mathematics
Keywords: Multiresolution analysis framework Dual frame wavelet Mask function Parseval frame wavelet
CLC: O174.2
Type: Master's thesis
Year: 2011
Downloads: 85
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Abstract


As an ideal time-frequency analysis tool, wavelet analysis is generated based on Fourier analysis and developed it effectively compensate for the deficiencies of Fourier analysis, harmonic analysis is seen as multi-crystalline half a century of work Because of its good adaptability and \further in-depth, is also expanding its scope of application of wavelet transform is a time-frequency localization tools, including continuous wavelet transform and discrete wavelet transform, and wavelet frame theory constitutes the main part of the discrete wavelet transform .1952 Duffin and Schaef-fer non-harmonic Fourier analysis in the study when first proposed the concept of Hilbert space frames, then Daubechies, Meyer, who will be introduced into the framework of wavelet theory, put forward the concept of wavelet frame wavelet framework of a wavelet kind of promotion and expansion, reducing the orthogonal wavelet basis of the requirements, the introduction of redundancy, so wavelet frame has a large degree of freedom in design, while the stability of redundancy in that, the robustness to noise orthogonal basis is superior due to both wavelet and wavelet frame framework excellent features, has now become a hot research scholars at home and abroad, in image processing, edge detection, noise removal, etc. shown great application potential, although For a discussion of wavelet framework has been related to various aspects of the theoretical study to be further improved, with good nature frame wavelet has yet our design. article focuses on the correlation properties of the wavelet framework to study the dual wavelet frames and Parseval wavelet frame structure, and portrayed with high vanishing moments wavelet frame, draw some conclusions to help the further development of the theory of wavelet frame full text is composed of four parts: Chapter 1: Introduction. briefly introduces the wavelet analysis and Development of the theory of wavelet frame and the latest research results. Chapter 2: wavelet frame and related properties first give the definition of a framework to discuss the relationship between frames and Riesz bases, defined by the frame operator dual frame is given the signal reconstruction formula, and finally discusses the framework for multi-resolution analysis of some properties of Chapter 3: dual wavelet frame structure. multiresolution analysis using the framework discussed dual wavelet frames and Parseval wavelet frame structure, given the specific Matrix Extension Methods Chapter 4: a high-level framework of vanishing moments of the wavelet characterizations. discussed the framework of vanishing moments of wavelet features, the use of oblique expansion principle constructed with high vanishing moments dual frame wavelet construction algorithm is given.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Fourier analysis ( classical harmonic analysis )
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