Numerical methods for edge-preserving image restoration.
Abstract: Many digital image applications rely on the image quality.
Unfortunately, images often are degraded by noise and blur during the formation,
transmission, and recording processes. Hence, image restoration is a necessary processing
step. Many current image restoration methods lose edge information while removing the
defects. This work focuses on developing accurate mathematical models ... read moreand efficient
numerical algorithms for edge-preserving image restoration problems. We first present a new
regularization parameter-choice algorithm broadly applicable to several image restoration
approaches, which is suitable for large-scale problems. Next, we consider three different
types of image restoration scenarios, and present algorithms for each. The first problem we
consider is image denoising. In particular, we explore the application of multigrid methods
in solving the nonlinear anisotropic diffusion denoising problem. Secondly, we introduce a
projection-based algorithm to solve image deblurring problem. For some applications, it is
necessary to solve a least squares problem with nonnegative constraints. Therefore, we also
present a novel multiplicative nonnegative least squares algorithm for image
super-resolution and color image labeling. The convergence analysis of each algorithm is
studied. Finally, we demonstrate the applications of the algorithms with many numerical
Thesis (Ph.D.)--Tufts University, 2012.
Submitted to the Dept. of Mathematics.
Advisor: Misha Kilmer.
Committee: Scott MacLachlan, Matthew Brand, and Thomas Hoft.
Keyword: Applied mathematics.read less