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Title: Low Dimensional Band-Limited Framelets and Their Applications in Colour Image Restoration
Authors: HOU LIKUN
Keywords: Band-limited, Framelets, Colour Image Restoration
Issue Date: 22-Apr-2013
Citation: HOU LIKUN (2013-04-22). Low Dimensional Band-Limited Framelets and Their Applications in Colour Image Restoration. ScholarBank@NUS Repository.
Abstract: This thesis consists of two major parts. The first part focuses on the theoretical study on the construction of band-limited framelets with good time-frequency localization property in low-dimensional Euclidean spaces. Based on the univariate Meyer's refinable function, this thesis provides a systematic approach to construct non-separable band-limited refinable functions, Riesz wavelets, orthonormal wavelets as well as wavelet tight frames (framelets) in 2D and 3D Euclidean spaces. With the newly constructed band-limited framelets in hand, the second part of the thesis focuses on the application of non-separable band-limited framelets and tensor-product spline framelets in colour image restoration. The main application explored in this thesis is on repairing over-exposed and under-exposed regions in regular digital colour photographs. By using wavelet tight frame based regularization methods and some tone mapping analogy, we develop in this thesis a comprehensive computational method to simultaneously (i) recover brightness values clipped due to over/under-exposure, (ii) enhance the contrast of under-exposed regions so that more visible image details could be revealed, and (iii) restore the chromatic values damaged due to over-exposure. Experimental results show that the proposed method outperforms existing approaches in the test data set.
Appears in Collections:Ph.D Theses (Open)

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