RUI: Adaptive Kernels for Partial Differential Equation Models in Image Denoising: Construction and Algorithms

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The investigator constructs adaptive kernels for diffusion PDE models in image denoising and develops kernel-based denoising algorithms. An adaptive kernel is a kernel that adaptively changes its kernel characteristics depending on the image content within a local window. Discrete kernels are filters, which are widely used in industrial image processing; and non-iterative filters can realize the real-time denoising. The proposed adaptive kernels are mainly derived from PDE models. Due to Rudin-Osher-Fatemi's influential work, there are a considerable number of PDE models for image denoising. Based on the extensive results in numerical analysis, highly accurate and stable algorithms have been developed. However, most numerical PDE algorithms involve either iteration or inverse matrices. They are time and/or memory consuming and therefore not suitable for real-time pre-processing noise reduction. The investigator studies the construction of adaptive kernels for some popular PDE models, designs parametric adaptive filters from these kernels, and develops algorithms for their implementations with emphasis on the extremely fast single-pass filter process. The investigator creates the GUI software to perform noise reduction based on the kernel-based algorithms, which provide a development kit suitable for industrial demands. The infinitesimal method is the main tool for the development of the adaptive kernels. He also applies Bayesian Decision Theory to create the rule for the optimal selection of the parameters in the adaptive filters, which are used to control the quality of noise reduction. This research support the national interest in NANOTECHNOLOGY and INFORMATION TECHNOLOGY due to the demand for digital images/videos for low-cost security cameras, mobile digital TV, cell-video phones, all of which are used for HOMELAND SECURITY and DEPARTMENT OF DEFENSE applications. The research also impacts feature-preserve noise reduction techniques, which is on the rise. On-line videos such as web-cams generally produce low-quality pictures. Even high-quality digital cameras and camcorders used in low-light or artificial-light environments produce noise. Feature-preserve noise reduction techniques provide a low-cost solution for enhancing these low-quality images. There are many types of software on the market for picture cleaning and computer enhancement, however mobile videos and similar products require real-time processing that can be built into the devices. The security demand for these techniques is very high, especially in U.S. Border areas, while the number of solutions are low. This project bridges the gulf between the highly developed theory and the underdeveloped industrial applications.