Structured Nonlinear Least Squares Problems in Biomedical and Biomolecular Imaging

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）成像的特定应用。在这个项目中处理的数学模型是困难的不适定逆问题。这些问题的计算解对数据中的误差非常敏感，并且对于大规模三维图像的实现是不平凡的。在这个项目中开发的新的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。利用非线性最小二乘问题的算法结构，以及在应用中产生的结构，将获得效率。与埃默里大学医学院和Winship癌症研究中心的研究人员合作，将用于测试和验证开发的方法，并将促进新软件向临床应用的过渡。改进图像重建和后期处理算法的断层合成可以对乳腺癌筛查产生深远的影响。除了提供比乳房x线照相术更好的筛查能力外，断层合成术对乳房的压迫更小（减轻了患者的身体疼痛），并且比计算机断层扫描（CT）需要更小的辐射剂量。除了应用于乳腺癌筛查之外，断层合成还可用于许多其他医学成像应用，其中使用标准x射线和CT。因此，这种应用的计算方法的进步可以在医学领域产生非常广泛的影响。在生物分子成像的情况下，改进的计算方法可以帮助提供廉价、准确的即时诊断成像系统。这可能严重影响对社会造成严重后果的感染的监测；例如，在世界贫穷地区管理感染艾滋病毒的病人。此外，本项目中考虑的应用（反卷积显微镜）可用于检查许多其他微观量，从而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。

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.