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。该项目中解决的数学模型是困难的不适定逆问题。这些问题的计算解决方案是非常敏感的数据中的错误，并实现大规模的三维图像是不平凡的。 本项目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，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来获得效率。 与埃默里大学医学院和Winship癌症研究中心的研究人员的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。改进的断层合成图像重建和后处理算法将对乳腺癌筛查产生深远的影响。除了提供比乳房X线摄影更好的筛查能力之外，断层合成需要更少的乳房压迫（减少患者的身体疼痛），并且它需要比计算机断层扫描（CT）更小的辐射剂量。 除了其在乳腺癌筛查中的应用之外，断层合成还可以用于使用标准X射线和CT的许多其他医学成像应用。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但准确的即时诊断成像系统。这可能会严重影响对社会产生严重后果的感染的监测，例如世界贫困地区艾滋病毒感染患者的管理。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，因此开发提供更好和更快重建的新算法，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.