Statistical Analysis of Image Restoration and Its Applications in Magnetic Resonance Imaging

图像恢复统计分析及其在磁共振成像中的应用

• 批准号: 0706082
• 负责人: Peihua Qiu
• 金额: --
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706082&HistoricalAwards=false
• 关键词: Statistical; Analysis; Image; Restoration; Its

Image analysis is an interdisciplinary research area with broad applications. One major focus of this project is on image deblurring when an observed image has both pointwise noise and spatial blur and when the blurring mechanism is unknown, which is often referred to as the blind image deblurring problem. In the statistical literature, little existing discussion can be found on image deblurring. In the applied mathematics and computer sciences literatures, existing image deblurring methods assume that the blurring mechanism, described by a point spread function, either is completely known, or follows a parametric model with one or more unknown parameters, or satisfies various conditions some of which are too restrictive to satisfy in applications. This project proposes alternative approaches to the blind image deblurring problem without imposing restrictive assumptions on the point spread function. The major idea is to estimate the point spread function from an observed test image or portions of an observed image with simple image structure, and then to restore true images using the estimated point spread function. If test images or portions of an observed image with simple image structure are not available, then the investigator suggests using the above idea locally, based on the observation that a true image can be well approximated by a simple structured one in a local neighborhood. Such local deblurring procedures allow the blurring mechanism to vary over location. In recent years, magnetic resonance imaging (MRI) is widely used for demonstrating pathological or other physiological alterations of living tissues. Due to movement of the imaged object and many other reasons, observed MRI images usually contain various contaminations, among which spatial blur and pointwise noise are most common. Right now, people usually use existing image deblurring techniques to deblur MRI images of individual 2-dimensional (2-D) slices of the imaged object slice by slice. This project suggests treating 2-D MRI images of different slices as profiles of a 3-D image and deblurring the 3-D image directly, after generalizing the proposed 2-D deblurring methods to 3-D cases, which would greatly improve the quality of the restored MRI images. This project also suggests using observed data in both frequency domain and spatial domain, and making use of their major strengths.This project would have broader impacts on the society through its impacts on the progress of image deblurring techniques. Proposed deblurring procedures should greatly improve the quality of restored MRI images, which should help people better understand living tissues and neural activities of humans and other animals and diagnose various diseases more accurately. Besides MRI and functional MRI, image deblurring is used widely elsewhere. For instance, it is used in machine recognition of handwriting, including machine reading of postal addresses, bank checks, and so forth. It is also used in preprocessing satellite images and various other images in medical sciences, meteorology, oceanography, military, space communication, etc. Therefore, this project could have a positive impact in all these areas. This project would also contribute to the development of human resources in science and engineering through its educational activities. For instance, the investigator will offer an advanced topics course on image analysis, from which graduate students from various departments will get systematic training in all aspects of scientific research. A web page will be created at the end of this project to include all computer programs and research results so that other researchers can easily download and use them. A Ph.D. student of the investigator is currently writing his thesis on image processing. All these educational activities should have a great impact on the popularity and further development of the related research areas.

图像分析是一个应用广泛的跨学科研究领域。本项目的一个主要焦点是当观察到的图像同时具有点向噪声和空间模糊以及模糊机制未知时的图像去模糊，这通常被称为盲图像去模糊问题。在统计文献中，很少有关于图像去模糊的讨论。在应用数学和计算机科学文献中，现有的图像去模糊方法假设模糊机制是完全已知的，或者是遵循一个或多个未知参数的参数模型，或者是满足各种条件，其中一些条件在应用中过于严格而无法满足。该项目提出了一种替代方法来解决盲图像去模糊问题，而不需要对点扩散函数施加限制性假设。该方法的主要思想是从观察到的测试图像或具有简单图像结构的观察图像的部分估计点扩展函数，然后使用估计的点扩展函数恢复真实图像。如果没有测试图像或具有简单图像结构的观察图像的部分，那么研究者建议在局部使用上述想法，基于观察到真实图像可以通过局部邻域中的简单结构图像很好地近似。这种局部去模糊程序允许模糊机制随位置而变化。近年来，磁共振成像（MRI）被广泛用于显示活体组织的病理或其他生理变化。由于被成像物体的运动等多种原因，观察到的MRI图像中通常含有各种污染，其中最常见的是空间模糊和点态噪声。目前，人们通常使用现有的图像去模糊技术来逐片去模糊成像对象的单个二维（2-D）切片的MRI图像。本项目建议将二维去模糊方法推广到三维病例后，将不同切片的二维MRI图像作为三维图像的轮廓处理，直接对三维图像进行去模糊处理，这将大大提高恢复的MRI图像的质量。本项目还建议在频域和空间域同时使用观测数据，并利用它们的主要优势。这个项目将通过对图像去模糊技术进步的影响对社会产生更广泛的影响。所提出的去模糊程序将大大提高恢复的MRI图像的质量，这将有助于人们更好地了解人类和其他动物的活体组织和神经活动，并更准确地诊断各种疾病。除MRI和功能性MRI外，图像去模糊在其他领域也得到了广泛的应用。例如，它用于手写的机器识别，包括邮政地址、银行支票等的机器读取。它还用于医学、气象学、海洋学、军事、空间通信等领域的卫星图像和各种其他图像的预处理。因此，这个项目可以在所有这些领域产生积极的影响。该项目还将通过其教育活动促进科学和工程方面人力资源的发展。例如，研究者将开设关于图像分析的高级专题课程，来自各个部门的研究生将在科学研究的各个方面得到系统的训练。在本项目结束时，将创建一个网页，包括所有计算机程序和研究结果，以便其他研究人员可以轻松下载和使用它们。该研究员的一名博士生目前正在撰写图像处理方面的论文。所有这些教育活动都将对相关研究领域的普及和进一步发展产生重大影响。