Computed Tomography and Sampling

计算机断层扫描和采样

• 批准号: 0709495
• 负责人: Adel Faridani
• 金额: $ 15.99万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0709495&HistoricalAwards=false
• 关键词: Computed; Tomography; Sampling

AbstractThe research proposed in this project involves Computed Tomography, Advanced Shannon Sampling Theory, applications of sampling theory in tomography, and combination of image reconstruction with image processing. Computed x-ray tomography produces images of opaque objects. The underlying mathematical problem consists of reconstructing a density function f(x) from finitely many measurements of its line integrals. Much of the present focus of the field is on fully three-dimensional imaging, stimulated by major algorithmic advances in recent years. Shannon sampling theory provides exact interpolation formulas for band-limited functions and plays a fundamental role in signal processing. It is used in tomography to identify efficient sampling schemes that allow for maximum resolution in the reconstructed images, as well as for error analysis of reconstruction algorithms. The research proposed in this project lies in the intersection of these areas and is motivated by applications. Its interconnected themes include the derivation of new sampling theorems; optimal data acquisition in 3D tomography; mathematically rigorous and practically useful analysis of recently developed 3D tomographic algorithms; local tomography in two and three dimensions; high-resolution reconstructions; and the close interaction of tomographic reconstruction with image processing, motivated by the experience that high-resolution reconstructions often carry more noise and can be further improved by state of the art image processing. In pursuing these themes the project will place an emphasis on interdisciplinary collaboration.Computed x-ray tomography (CT) is an increasingly popular technique for two- and three-dimensional (3D) imaging of opaque objects. An object is irradiated and the image is computed from measurements of the transmitted radiation. Beyond its famous use in medical imaging, tomography has found an increasing number of applications in science, engineering, and technology. The research undertaken in this project will contribute to make this technique even more efficient. It will develop and use Shannon type sampling theorems to identify optimal data acquisition schemes for 3D tomography and to analyze and improve algorithms for image reconstruction and image processing. This will contribute to the development of fully three-dimensional image reconstruction methods that require a minimal number of measurements and have high accuracy, optimal resolution, and minimal noise. The general approach taken in this project aims to unite research on fundamentals with interdisciplinary efforts driven directly by practical challenges presented by users of tomography. The project will also involve efforts to provide graduate students with an interdisciplinary environment centered around multi-dimensional imaging.

本课题的研究内容涉及计算机层析成像、先进香农采样理论、采样理论在层析成像中的应用以及图像重建与图像处理的结合。计算机X射线断层摄影产生不透明物体的图像。基本的数学问题包括从其线积分的大量测量重建密度函数f（x）。 该领域目前的重点是全三维成像，受到近年来主要算法进步的刺激。香农采样理论为带限函数提供了精确的插值公式，在信号处理中起着重要的作用。它用于断层扫描，以确定有效的采样方案，允许在重建图像的最大分辨率，以及重建算法的误差分析。 在这个项目中提出的研究是在这些领域的交叉点，是由应用程序的动机。其相互关联的主题包括新的采样定理的推导;三维层析成像中的最佳数据采集;最近开发的三维层析成像算法的数学上严格和实际有用的分析;二维和三维的局部层析成像;高分辨率重建;以及断层重建与图像处理的密切相互作用，这是由高分辨率重建通常携带更多噪声并且可以通过现有技术的图像处理来进一步改进的经验激发的。在追求这些主题的过程中，该项目将强调跨学科的合作。计算机X射线断层扫描（CT）是一种越来越受欢迎的技术，用于不透明物体的二维和三维（3D）成像。 照射对象，并且根据透射辐射的测量来计算图像。 除了其在医学成像中的著名用途外，断层扫描在科学，工程和技术方面的应用越来越多。在这个项目中进行的研究将有助于使这项技术更加有效。它将开发和使用香农型采样定理，以确定最佳的数据采集方案的三维断层扫描，并分析和改进算法的图像重建和图像处理。这将有助于开发全三维图像重建方法，这些方法需要最少的测量次数，并具有高精度，最佳分辨率和最小噪声。该项目采取的一般方法旨在将基础研究与由断层扫描用户提出的实际挑战直接驱动的跨学科努力相结合。 该项目还将努力为研究生提供一个以多维成像为中心的跨学科环境。