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

该项目涉及开发用于恢复因非线性和非均匀运动模糊而退化的图像的算法和软件。 研究者和他的同事要解决的问题包括开发非线性运动模糊的适当数学模型、分析模糊过程的病态、开发消除运动模糊的有效算法以及开发特定应用的软件。 需要算法和软件开发来解决在这些问题的离散公式中出现的大规模、严重病态的线性系统。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不适用。用于监视、医疗诊断和其他科学目的的图像很少是完美的。 成像系统的缺陷和环境影响可能会导致记录图像的严重退化，例如模糊。 为了获得更好质量的图像，通常需要后处理技术（即计算方法）。 设计适当的算法需要对图像形成过程进行精确的数学建模，并开发稳健、高效的计算工具。 图像模糊的最常见原因之一是记录设备或成像对象的运动。 尽管具有恒定速度和方向的线性运动已广为人知，但在开发数学模型和有效算法来恢复因非线性和非均匀运动模糊而劣化的图像方面所做的工作却很少。 研究者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应用于许多重要应用，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.