Non-local methods for DNA detection and image restoration
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Many methods have been developed for abnormal linear systems. However, these methods often assume locality for datasets; thus the features of the data cannot be extracted most efficiently to formulate models, which can lead to the loss of information and incorrect results. To overcome the disadvantages of locality methods, we develop new adaptive non-local data analysis methods for two kinds of linear systems and apply the methods to two applications: component detection in multiplexed Raman spectra and image restoration. The first application, which was a project sponsored by Renishaw, involves the detection of component dyes from an observed DNA spectrum. The second application is to approximate original scenes from observed images degraded by blurring and noise. In contrast to pointwise methods, our methods investigate patches or neighbourhoods in datasets and extract features from these patches for discrimination and denoising through correlation analysis of the similarity of patches. Inthisthesis, our methods are developed by combining non-local data analysis with many popular traditional algorithms, such as model selection with the maximum p-value, conjugate gradient descent and the iteration method of higher convergence order; therefore, our methods are general and can be utilised for further applications to other image processing problems.