Multispectral Tomosynthesis Imaging: Mathematical Models, Algorithms and Software

该项目专注于开发断层合成乳房图像重建的计算方法，这是一种使用略微改进的传统X射线系统重建三维图像的技术。这个项目中涉及的数学模型是困难的不适定反问题；计算解对数据中的误差非常敏感，并且对大规模三维图像的实现是不平凡的。所有以前的乳房合成图像重建算法都使用一个简化的、但不正确的假设，即源X射线束是由具有恒定能量的光子组成的，即假设X射线束是单能的。简化的单能假设导致了一个线性数学模型。这个项目使用了物理上正确的，因此也更准确的假设，即x射线束是多能量的。由此产生的数学模型是非线性的，这给数学模型的开发和分析以及计算方法的发展带来了巨大的挑战。然而，正如这个项目揭示的那样，非线性模型允许重建的图像的伪影比线性模型少得多。此外，非线性模型可以结合参数化，允许将乳房显式分解成不同的物质，如腺组织、脂肪组织、钙化和碘化造影剂，从而提供更好的诊断信息。在美国，每年有超过20万名妇女被诊断为乳腺癌，但如果癌症是局部的，如果它在扩散到身体其他部位之前被发现，五年存活率有97%。因此，有助于早期发现和诊断乳腺癌的改进的成像技术可以对女性的医疗保健产生深远的影响。该项目的研究重点是断层合成成像，该成像在2011年刚刚获得FDA批准用于临床，因为它有可能提供比乳房X光摄影更好的筛查能力。这项工作中开发的新的数学和计算方法旨在锁定断层合成技术对乳腺癌筛查的潜在变革性好处，为医生提供显著更好的诊断信息。除了在乳腺癌筛查中的应用外，断层合成在其全身实施中还可以用于许多其他使用标准X射线和CT的应用，例如用于检测肺结节的胸部成像，以及诸如核废料检查和爆炸检测的非医学成像应用。因此，这一应用的计算方法的进步可以在成像领域产生非常广泛的影响。数学和计算机科学的研究人员与埃默里大学放射和成像科学系和Winship癌症研究所的研究人员之间的合作促进了将新软件应用于临床。

This project focuses on the development of computational methods fortomosynthesis breast image reconstruction, a technique used toreconstruct 3-dimensional images using slightly modified versions ofconventional x-ray systems. The mathematical models addressed in thisproject are difficult ill-posed inverse problems; computed solutionsare very sensitive to errors in the data, and implementation for largescale 3-dimensional images is nontrivial. All previous breasttomosynthesis image reconstruction algorithms use a simplified, butincorrect assumption that the source x-ray beam is comprised ofphotons with a constant energy; that is, the x-ray beam is assumed tobe monoenergetic. The simplified monoenergetic assumption results ina linear mathematical model. This project uses the physicallycorrect, and hence more accurate, assumption that the x-ray beam ispolyenergetic. The resulting mathematical model is nonlinear,providing great challenges to the development and analysis ofmathematical models, as well as for the development of computationalmethods. However, as this project reveals, the nonlinear model allowsfor reconstructing images with substantially fewer artifacts than thelinear model. Moreover, the nonlinear model can incorporateparameterizations to allow for explicit decomposition of the breastinto distinct materials, such as, glandular tissue, adipose tissue,calcifications, and iodinated contrast agents, thereby providingimproved diagnostic information.In the US, over 200,000 women are diagnosed with breast cancer everyyear, but there is a 97% five-year survival rate if the cancer islocalized, and if it is discovered before it spreads to other parts ofthe body. Therefore, improved imaging techniques that help to detectand diagnose breast cancer early can have a profound impact on thehealthcare of women. The research in this project focuses ontomosynthesis imaging, which just received FDA approval for clinicaluse in 2011, because it has the potential to provide substantiallybetter screening capabilities than mammography. The new mathematicaland computational approaches developed in this work are designed tounlock the potentially transformative benefits of tomosynthesis forbreast cancer screening, providing significantly better diagnosticinformation to physicians. In addition to its application to breastcancer screening, tomosynthesis, in its whole-body implementation canbe used for many other applications where standard x-ray and CT areused, such as chest imaging for detection of lung nodules, as well asnon-medical imaging applications such as nuclear waste inspections andexplosive detection. Thus, advances in computational methods for thisapplication can have a very broad impact in the imaging field.Collaborations between researchers in Mathematics and Computer Scienceand researchers in the Department of Radiology and Imaging Sciencesand Winship Cancer Institute at Emory University facilitatestransitioning new software to clinical use.