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10/27/06 Colloquium
Professor Charles Chui
Stanford University and University of Missouri-St. Louis
Stanford University and University of Missouri-St. Louis
Image Noise Removal based on the Variational Approach and Wavelets
Abstract: The background of this work is the standard problem of minimization of some total energy functional, but with specific choices of the internal energy density functions g(x). Our interest in this study is motivated by the search of effective solutions to certain inverse problems, particularly for real-time image noise removal for digital cameras. In general, depending on the objectives of the inverse problems under investigation, such as curve fitting, image noise removal, and feature extraction, the internal energy in our study is governed by g( | Lu | ); with (Lu) (x) = u´´ (x), (Lu) (x,y) = (Grad u) (x,y), and Lu being some wavelet transform of u in any dimension. For digital image noise removal, in particular, a suitable choice of g(x) leads to the anisotropic diffusion model, the discretization of which, in turn, is relevant to the design of certain content-dependent filters, notably the bilateral filters. A natural generalization of this approach also gives rise to the notions of diffusion maps and geometric harmonics that constitute the foundation for the recent research investigations in diffusion wavelets for analyzing complex data in high dimensions. This talk is based on his joint work with Jianzhong Wang.