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Summary of research output from DOE grant DE-FG02-92ER45471 during the period 1992-2006: publications, invited talks, conference organization, and PhD students graduated.

Description: In this report I summarize some of the main results obtained during the present grant period. They are: (1) Orientation selection in dendritic evolution; (2) Globubar-dendritic transition; and (3) Physics and prediction of grain boundary mobility.
Date: August 1, 2006
Creator: Karma, Alain, PhD.
Partner: UNT Libraries Government Documents Department

An Adaptive B-Spline Method for Low-order Image Reconstruction Problems - Final Report - 09/24/1997 - 09/24/2000

Description: A common problem in signal processing is to estimate the structure of an object from noisy measurements linearly related to the desired image. These problems are broadly known as inverse problems. A key feature which complicates the solution to such problems is their ill-posedness. That is, small perturbations in the data arising e.g. from noise can and do lead to severe, non-physical artifacts in the recovered image. The process of stabilizing these problems is known as regularization of which Tikhonov regularization is one of the most common. While this approach leads to a simple linear least squares problem to solve for generating the reconstruction, it has the unfortunate side effect of producing smooth images thereby obscuring important features such as edges. Therefore, over the past decade there has been much work in the development of edge-preserving regularizers. This technique leads to image estimates in which the important features are retained, but computationally the y require the solution of a nonlinear least squares problem, a daunting task in many practical multi-dimensional applications. In this thesis we explore low-order models for reducing the complexity of the re-construction process. Specifically, B-Splines are used to approximate the object. If a ''proper'' collection B-Splines are chosen that the object can be efficiently represented using a few basis functions, the dimensionality of the underlying problem will be significantly decreased. Consequently, an optimum distribution of splines needs to be determined. Here, an adaptive refining and pruning algorithm is developed to solve the problem. The refining part is based on curvature information, in which the intuition is that a relatively dense set of fine scale basis elements should cluster near regions of high curvature while a spares collection of basis vectors are required to adequately represent the object over spatially smooth areas. The pruning part is a greedy ...
Date: April 11, 2000
Creator: Li, Xin; Miller, Eric L.; Rappaport, Carey & Silevich, Michael
Partner: UNT Libraries Government Documents Department