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Modeling, Analysis, and Implementation of Finite Difference Schemes for Nonlinear Diffusion with Applications to Image Processing

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dc.contributor.advisor Seshaiyer, Padmanabhan
dc.contributor.author Franklin, Armelle S.
dc.creator Franklin, Armelle S.
dc.date 2013-05-02
dc.date.accessioned 2013-08-13T17:50:41Z
dc.date.available NO_RESTRICTION en_US
dc.date.available 2013-08-13T17:50:41Z
dc.date.issued 2013-08-13
dc.identifier.uri https://hdl.handle.net/1920/8293
dc.description.abstract This thesis proposes to model, analyze and implement a nonlinear diffusion model problem for reduction in noise and speckle in image processing applications. Specifically, the Perona-Malik model equation that is widely studied in the image processing community is implemented via explicit and implicit finite difference algorithms. The solution methodology converts discrete image data onto a finer non-uniform grid space via interpolation techniques and applies the proposed numerical algorithms to reduce noise. These numerical algorithms are investigated analytically and computationally for appropriate choices of nonlinear diffusion coefficient functions. We derived conditions for stability and convergence of the proposed numerical algorithms. Numerical experiments are presented on benchmark problems that show the robustness and reliability of the proposed numerical schemes.
dc.language.iso en en_US
dc.subject finite difference en_US
dc.subject image processing en_US
dc.subject Perona-Malik en_US
dc.subject nonlinear diffusion en_US
dc.subject noise reduction en_US
dc.subject speckle en_US
dc.title Modeling, Analysis, and Implementation of Finite Difference Schemes for Nonlinear Diffusion with Applications to Image Processing en_US
dc.type Thesis en
thesis.degree.name Master of Science in Mathematics en_US
thesis.degree.level Master's en
thesis.degree.discipline Mathematics en
thesis.degree.grantor George Mason University en


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