Multispectral Tomosynthesis Imaging: Mathematical Models, Algorithms and Software

这个项目的重点是发展计算方法的断层合成乳房图像重建，一种技术用于重建三维图像使用稍微修改版本的传统x射线系统。在这个项目中解决的数学模型是困难的不适定的反问题，计算的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。 所有以前的乳腺断层合成图像重建算法都使用一个简化但不正确的假设，即源X射线束由具有恒定能量的光子组成;也就是说，X射线束被假设为单能的。 简化的单能假设是线性数学模型的结果。 这个项目使用了物理上正确的，因此更准确的假设，即x射线束是多能的。 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，正如该项目所揭示的，非线性模型允许重建图像，其伪影比线性模型少得多。 此外，非线性模型可以简化参数化，以允许将乳房明确分解为不同的材料，例如腺体组织、脂肪组织、钙化和碘化造影剂，从而提供改进的诊断信息。在美国，每年有超过20万名妇女被诊断患有乳腺癌，但如果癌症是局部的，五年生存率为97%，如果在它扩散到身体其他部位之前被发现。 因此，有助于早期检测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光检查更好的筛查能力。在这项工作中开发的新的南极和计算方法旨在锁定乳腺癌筛查的断层合成的潜在变革性益处，为医生提供更好的诊断信息。 除了其在乳腺癌筛查中的应用之外，断层合成在其全身实施中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，以及非医学成像应用，例如核废料检查和爆炸检测。 因此，这种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学和成像科学系以及Winship癌症研究所的研究人员之间的合作促进了新软件的临床应用。

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.