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

本计画主要针对非线性及非均匀运动模糊所造成之影像复原，进行演算法与软体之发展。 研究者和他的同事们要解决的问题包括发展一个合适的非线性运动模糊的数学模型，分析模糊过程的病态，发展有效的算法来消除运动模糊，以及开发特定应用的软件。 需要算法和软件开发来解决这些问题的离散公式中出现的大规模、严重病态线性系统。对于非线性和非均匀运动，这些系统通常没有可利用的结构，也就是说，使用快速傅立叶变换的标准反卷积技术是不适用的。用于监视、医疗诊断和其他科学目的的图像很少是完美的。 成像系统的缺陷和不利的心理影响可能会导致严重的退化，如模糊，在记录的图像。 后处理技术（即，计算方法）通常是获得更好的图像质量所必需的。 设计合适的算法需要对图像形成过程进行精确的数学建模，并开发出鲁棒、高效的计算工具。 造成图像模糊的最常见原因之一是记录设备或被成像物体的运动。 虽然直线运动，具有恒定的速度和方向，是很好的理解，很少的工作beendone开发的数学模型和有效的算法，恢复图像退化的非线性和非均匀motionblurs。 研究人员和他的同事认为这个问题既困难又重要。 通过该项目开发的软件可以应用于许多重要的应用，包括医学成像（例如，心脏成像过程中心脏的运动）、空中和视频监控、法医调查和天文成像。

This project is concerned with the development of algorithms andsoftware for the restoration of images degraded by nonlinear andnonuniform motion blurs. The problems to be addressed by theinvestigator and his colleagues include the development of anappropriate mathematical model for nonlinear motion blurs, analysis ofthe ill-conditioning of the blurring process, development of efficientalgorithms for removing motion blur, and development of software forspecific applications. Algorithm and software development is neededfor the solution of large scale, severely ill-conditioned linearsystems that arise in the discrete formulation of these problems. Fornonlinear and nonuniform motion, these systems generally have noexploitable structure; that is, standard deconvolution techniques thatuse fast Fourier transforms are not applicable. Images used for surveillance, medical diagnostic, and other scientificpurposes are rarely perfect. Imperfections in the imaging system andenvironmental effects may result in serious degradations, such asblurring, in the recorded image. Postprocessing techniques (i.e.,computational methods) are often necessary to obtain better qualitypictures. Designing appropriate algorithms requires accuratemathematical modeling of the image formation process, and developmentof robust, efficient computational tools. One of the most commoncauses of blurring in images is motion of either the recording deviceor the objects being imaged. Although linear motion, with constantspeed and direction, is well understood, very little work has beendone to develop mathematical models and efficient algorithms for therestoration of images degraded by nonlinear and nonuniform motionblurs. The investigator and his colleagues consider this difficult,important problem. The software developed through this project can beapplied to many important applications, including medical imaging(e.g., movement of the heart during cardiac imaging processes), aerialand video surveillance, forensic investigations, and astronomicalimaging.