Images Degraded by Nonlinear Motion Blurs: Mathematical Models, Algorithms and Applications

Emory University, Atlanta GA

Investigators

Abstract

This project is concerned with the development of algorithms and software for the restoration of images degraded by nonlinear and nonuniform motion blurs. The problems to be addressed by the investigator and his colleagues include the development of an appropriate mathematical model for nonlinear motion blurs, analysis of the ill-conditioning of the blurring process, development of efficient algorithms for removing motion blur, and development of software for specific applications. Algorithm and software development is needed for the solution of large scale, severely ill-conditioned linear systems that arise in the discrete formulation of these problems. For nonlinear and nonuniform motion, these systems generally have no exploitable structure; that is, standard deconvolution techniques that use fast Fourier transforms are not applicable. Images used for surveillance, medical diagnostic, and other scientific purposes are rarely perfect. Imperfections in the imaging system and environmental effects may result in serious degradations, such as blurring, in the recorded image. Postprocessing techniques (i.e., computational methods) are often necessary to obtain better quality pictures. Designing appropriate algorithms requires accurate mathematical modeling of the image formation process, and development of robust, efficient computational tools. One of the most common causes of blurring in images is motion of either the recording device or the objects being imaged. Although linear motion, with constant speed and direction, is well understood, very little work has been done to develop mathematical models and efficient algorithms for the restoration of images degraded by nonlinear and nonuniform motion blurs. The investigator and his colleagues consider this difficult, important problem. The software developed through this project can be applied to many important applications, including medical imaging (e.g., movement of the heart during cardiac imaging processes), aerial and video surveillance, forensic investigations, and astronomical imaging.