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Title of the thesis: Edge structure preserving 2-D and 3-D image denoising by jump surface estimation.
Primary contribution of the thesis: This thesis utilizes jump regression analysis to advance a new class of denoising methodologies for 2-D and 3-D images, with a particular emphasis on faithfully preserving intricate edge structures. By moving beyond the limitations of many existing denoising tools, the proposed approaches aim to enhance structural interpretability in noisy imaging environments. While the thesis primarily addresses additive noise, it also extends its scope to tackle non-additive Rician noise, a pervasive challenge in magnitude MRI imaging, thereby broadening the applicability of the proposed framework to real-world medical imaging contexts.