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Skip to Search Results- 5Wavelets
- 2Directionality
- 1Ball's integral inequality
- 1Biorthogonal multiwavelets
- 1Compressive Sensing
- 1Difference schemes
- 1Alexander, Litvak (Department of Mathematical and Statistical Sciences)
- 1Bin Han (Mathematical and Statistical Sciences)
- 1Han, Bin (Mathematical and Statistical Sciences)
- 1Jia, Rong-Qing (Mathematical and Statistical Sciences)
- 1Jia, Rong-Qing (Mathematics)
- 1Wong, Yau Shu (Mathematical and Statistical Sciences)
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Spring 2014
This thesis is mostly based on six papers on selected topics in Asymptotic Geometric Analysis, Wavelet Analysis and Applied Fourier Analysis. The first two papers are devoted to Ball's integral inequality. We prove this inequality via spline functions. We also provide a method for computing all...
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Fall 2010
In this thesis, we develop some new models and efficient algorithms for image denoising. The total variation model of Rudin, Osher, and Fatemi(ROF) for image denoising is considered to be one of the most successful deterministic denoising models. It exploits the non-smooth total variation (TV)...
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Fall 2010
In Chapters 1 and 2, we introduce the definition of interpolating refinable function vectors in dimension one and high dimensions, characterize such interpolating refinable function vectors in terms of their masks, and derive their sum rule structure explicitly. We study biorthogonal refinable...
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Fall 2015
This thesis concentrates on the construction of directional tensor product complex tight framelets. It uses a complex tight framelet filter bank in one dimension and the tensor product of the one-dimensional filter bank to obtain high-dimensional filter bank. It has a number of advantages over...
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Fall 2010
In this thesis, we investigate Riesz bases of wavelets and their applications to numerical solutions of elliptic equations. Compared with the finite difference and finite element methods, the wavelet method for solving elliptic equations is relatively young but powerful. In the wavelet Galerkin...