Elliptical Radon Transforms in Image Reconstruction

图像重建中的椭圆氡变换

• 批准号: 1109417
• 负责人: Gaik Ambartsoumian
• 金额: $ 17.59万
• 依托单位: University of Texas at Arlington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109417&HistoricalAwards=false
• 关键词: Elliptical; Radon; Transforms; Image; Reconstruction

The principal investigator of this project and his collaborator study elliptical Radon transforms (ERT), which play an important role in bi-static models of various imaging modalities such as near-field ultrasound tomography, synthetic aperture radar, geophysical exploration imaging, and sonar. Bi-static data acquisition geometries involve separate emitter and receiver to image a medium using signals such as acoustic or electromagnetic waves. This approach offers several advantages. In the case of radar imaging the receivers are passive; hence separating their motion from the active emitters allows receivers alone to be flown in an unsafe environment. In sonar, data collection involves the receivers towed behind the boat transmitting the sound source. In ultrasound tomography separate emitter and receiver can provide data sets, for example, of high angular resolution. Assuming constant speed of wave propagation in the medium, the mathematical model for all these modalities is expressed through the ERT defined by integrals of an unknown function over ellipsoids or ellipses. The investigators develop image reconstruction techniques for several imaging modalities based on such elliptical Radon transforms. The principal mathematical problems they address include: development of microlocal analysis of ERT in various practically important data acquisition geometries, development of exact and approximate inversion formulas and algorithms for ERT, description of injectivity sets, and range characterization of ERT, i.e. the characterization of consistency conditions for the data for the aforementioned imaging modalities. The investigators test the results of their research in laboratory ultrasound experiments performed by their collaborators in radiology and biomedical engineering.The principal investigator and his collaborator solve image reconstruction problems that are of great importance in several fields including ultrasonic reflectivity imaging in medicine, geophysical exploration, sonar and synthetic aperture radar imaging. Many of these problems have similar mathematical representation, and the investigators develop solutions as well as derive numerical algorithms for such problems. The goals and novel results of this project provide a positive impact on healthcare technologies (e.g. early detection of cancer), national security (e.g. improved radar systems), economics (e.g. improved geophysical exploration, or industrial nondestructive testing), and for many other fields of modern life, where the use of remote sensing and imaging has become an indispensable tool. The investigators work with their collaborators to test the results of their research in laboratory ultrasound experiments. The investigators advise and mentor students on research topics directly related to this proposal, and train future specialists of the field. They are committed to graduate and undergraduate teaching and engage students from underrepresented groups in the form of introductory workshops, tutorials and short courses. The investigators broadly disseminate the results of the project through publications in selected scientific journals and presentations at conferences.

该项目的主要研究者和他的合作者研究椭圆Radon变换（ERT），它在近场超声断层扫描，合成孔径雷达，地球物理勘探成像和声纳等各种成像模式的双基地模型中发挥着重要作用。双基地数据采集几何结构涉及单独的发射器和接收器，以使用诸如声波或电磁波的信号对介质进行成像。这种方法有几个优点。在雷达成像的情况下，接收器是无源的;因此，将它们的运动与有源发射器分开，可以让接收器单独在不安全的环境中飞行。在声纳中，数据收集涉及拖曳在船后发送声源的接收器。在超声断层摄影中，单独的发射器和接收器可以提供例如高角度分辨率的数据集。假设波在介质中的传播速度恒定，所有这些模态的数学模型通过由椭球或椭圆上的未知函数的积分定义的ERT来表示。研究人员开发的图像重建技术的几种成像方式的基础上，这种椭圆拉东变换。他们解决的主要数学问题包括：在各种实际上重要的数据采集几何的ERT的微局部分析的发展，精确和近似的反演公式和算法的ERT，注入集的描述，和ERT的范围表征，即上述成像方式的数据的一致性条件的表征。研究人员在放射学和生物医学工程的合作者进行的实验室超声实验中测试他们的研究结果。首席研究员和他的合作者解决了在医学超声反射成像、地球物理勘探、声纳和合成孔径雷达成像等多个领域非常重要的图像重建问题。许多这些问题有类似的数学表示，和调查人员开发解决方案，以及获得数值算法等问题。该项目的目标和新成果对医疗保健技术（例如癌症的早期检测）、国家安全（例如改进的雷达系统）、经济（例如改进的地球物理勘探或工业无损检测）以及现代生活的许多其他领域产生了积极影响，其中遥感和成像的使用已成为不可或缺的工具。研究人员与他们的合作者一起在实验室超声实验中测试他们的研究结果。研究人员就与本提案直接相关的研究课题向学生提供建议和指导，并培养该领域未来的专家。他们致力于研究生和本科教学，并以介绍性研讨会，辅导和短期课程的形式吸引来自代表性不足群体的学生。调查人员通过在选定的科学期刊上发表文章和在会议上发表演讲，广泛传播项目成果。