Structured Nonlinear Least Squares Problems in Biomedical and Biomolecular Imaging

生物医学和生物分子成像中的结构化非线性最小二乘问题

• 批准号: 0811031
• 负责人: James Nagy
• 金额: $ 29.74万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0811031&HistoricalAwards=false
• 关键词: Structured; Nonlinear; Least; Squares; Problems

This project has significant mathematical and computational challenges, and at the same time is focused on specific applications in biomedical (tomosynthesis) and biomolecular (microscopy) imaging.The mathematical models addressed in this project are difficult ill-posed inverse problems. Computed solutions of these problems are very sensitive to errors in the data, and implementation for large scale 3-dimensional images is nontrivial. New image post processing algorithms developed in this project will be based on computing solutions of large scale structured nonlinear least squares problems.Efficiency will be obtained by exploiting algorithmic structure of the nonlinear least squares problem, as well as structure that arises in the applications. Collaborations with researchers in the School of Medicine and Winship Cancer Research Center at Emory University will be used to test and verify developed methods, and will facilitate efforts to transition new software to clinical use.Improved image reconstruction and post processing algorithms for tomosynthesis can have a profound impact on breast cancer screening. In addition to providing better screening capabilities than mammography, tomosynthesis requires less compression of the breast (reducing physical pain to the patient), and it requires a smaller radiation dose than computed tomography (CT). In addition to its application to breast cancer screening, tomosynthesis can be used for many other medical imaging applications where standard x-ray and CT are used. Thus, advances in computational methods for this application can have a very broad impact in the medical field. In the case of biomolecular imaging, improved computational approaches can help provide inexpensive, yet accurate, point-of-care diagnostic imaging systems. This can significantly impact the monitoring of infections that have serious consequences to society; for example, management of HIV infected patients in poor regions of the world. Moreover, the application considered in this project (deconvolution microscopy), can be used to examine many other microscopic quantities, and thus development of new algorithms that provide better and faster reconstructions, can have a broad impact in many scientific fields, including biology, chemistry, neuroscience, and physics.

该项目具有重大的数学和计算挑战，同时专注于生物医学（断层合成）和生物分子（显微镜）成像中的特定应用。该项目中解决的数学模型是困难的不适定反问题。这些问题的计算解决方案对数据中的错误非常敏感，并且大规模 3 维图像的实现并非易事。 该项目开发的新图像后处理算法将基于大规模结构化非线性最小二乘问题的计算解决方案。通过利用非线性最小二乘问题的算法结构以及应用中出现的结构，将获得效率。 与埃默里大学医学院和温希普癌症研究中心的研究人员的合作将用于测试和验证开发的方法，并将促进将新软件过渡到临床使用的努力。改进的断层合成图像重建和后处理算法可以有对乳腺癌筛查产生深远影响。除了提供比乳房 X 光检查更好的筛查能力外，断层合成需要更少的乳房受压（减少患者的身体疼痛），并且比计算机断层扫描 (CT) 需要的辐射剂量更小。 除了应用于乳腺癌筛查之外，断层合成还可用于使用标准 X 射线和 CT 的许多其他医学成像应用。因此，该应用的计算方法的进步可以对医学领域产生非常广泛的影响。 就生物分子成像而言，改进的计算方法可以帮助提供廉价但准确的即时诊断成像系统。这可能会严重影响对社会造成严重后果的感染的监测；例如，对世界贫困地区艾滋病毒感染者的管理。此外，该项目中考虑的应用（反卷积显微镜）可用于检查许多其他微观量，因此开发提供更好更快重建的新算法可以在许多科学领域产生广泛影响，包括生物学、化学、神经科学和物理学。