Mathematical approaches to digital color image denoising
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Many mathematical models have been designed to remove noise from images. Most of them focus on grey value images with additive artificial noise. Only very few specifically target natural color photos taken by a digital camera with real noise. Noise in natural color photos have special characteristics that are substantially different from those that have been added artificially. In this thesis previous denoising models are reviewed. We analyze the strengths and weakness of existing denoising models by showing where they perform well and where they don't. We put special focus on two models: The steering kernel regression model and the non-local model. For Kernel Regression model, an adaptive bilateral ﬁlter is introduced as complementary to enhance it. Also a non-local bilateral filter is proposed as an application of the idea of non-local means ﬁlter. Then the idea of cross-channel denoising is proposed in this thesis. It is effective in denoising monochromatic images by understanding the characteristics of digital noise in natural color images. A non-traditional color space is also introduced specifically for this purpose. The cross-channel paradigm can be applied to most of the exisiting models to greatly improve their performance for denoising natural color images.