Thesis (Ph. D.)--University of Wisconsin--Madison, 1971. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M. Sc.)--University of the Western Cape, 2007. / Includes bibliographical references (leaves 61-77).

Thesis (M.S.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaf 54).

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 238-250). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1991. / "June 1991." Includes bibliographical references (p. 266-273).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Graduate

No description available.

With the increased presence of image-based data in modern applications, the need for robust methods of image denoising grows greater. The work presented herein considers two of the most ubiquitous approaches towards image denoising: variational and non-local methods. The effectiveness of these methods is assessed using quantitatively using peak signal-to-noise ratio and structural similarity index measure metrics. This study employs ��−means clustering, an unsupervised machine learning algorithm, to isolate the most dominant cluster centroids within the incoming data and propose the introduction of a new adaptive parameter into the non-local means framework. Motivated by the fact that a majority of discrepancies between clean and denoised images occur at feature edges, this study examines several convolution-based edge detection methods to isolate relevant feature. The resultant gradient and edge information is used to further parameterize the ��−means non-local method. An additional hybrid method involving the combined contributions of variational and ��−means non-local denoising is proposed, with the weighting determined by edge intensities. This method outperforms the other methods outlined in the study, both conventional and newly presented.

Numerical methods for solving initial value problems in ordinary differential equations are studied. A notation is introduced to represent cyclic methods in terms of two matrices, A_h, and B_h, and this is developed to cover the very extensive class of m-block methods. Some stability results are obtained and convergence is analysed by means of a new consistency concept, namely optimal consistency. It is shown that optimal consistency allows one to give two-sided bounds on the global error, and examples are given to illustrate this. The form of the inverse of A_h is studied closely to give a criterion for the order of convergence to exceed that of consistency by one. Further convergence results are obtained , the first of which gives the orders of convergence for cases in which A_h, and B_h, have a special form, and the second of which gives rise to the possibility of the order of convergence exceeding that of consistency by two or more at some stages. In addition an alternative proof is given of the superconvergence result for collocation methods. In conclusion the work covered is set in the context of that done in recent years by various authors.