Mathematical Sciences: Iterative Methods for Image Processing

点击翻译按钮获取中文摘要

This career advancement award supports mathematical research in the field of iterative methods for large systems of equations arising in image processing. Application to image processing and medical imaging is planned. The central problem of image restoration is the estimation of the original image, given a version of the image degraded by noise and blur. Work will be done developing and analyzing new fast algorithms for the computation of the estimated image. Two different approaches to image restoration predominate, (i) algebraic restoration, viewed as a linear, possibly ill-conditioned, system of equations and (ii) stochastic restoration where one regards the problem of estimating vectors subject to random disturbances. Numerical methods for both approaches will be developed. Either approach yields linear systems of equations that have a structure that can be used in the development and analysis of efficient algorithms for image restoration. The structure depends on the assumptions made on the image and the noise. The matrices in these systems are typically quite large. The computational work, even with efficient methods, is demanding. Since many applications require real-time image restoration, the development of algorithms for parallel computers is important. Work done on this project focuses on the development of iterative methods that lend themselves will to implementation on multiprocessors.