Multispectral Tomosynthesis Imaging: Mathematical Models, Algorithms and Software

该项目侧重于开发乳腺断层合成图像重建的计算方法，这是一种使用传统x射线系统的稍微修改版本来重建三维图像的技术。在这个项目中处理的数学模型是困难的病态逆问题；计算的解决方案对数据中的错误非常敏感，并且对于大规模三维图像的实现是非平凡的。以前所有的乳房断层合成图像重建算法都使用了一个简化但正确的假设，即源x射线束由具有恒定能量的光子组成；也就是说，假定x射线束是单能的。简化的单能假设得到线性数学模型。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，这对数学模型的发展和分析以及计算方法的发展都提出了很大的挑战。然而，正如这个项目所揭示的那样，非线性模型允许用比线性模型少得多的伪影重建图像。此外，非线性模型可以结合参数化，以便将乳房明确分解为不同的物质，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20万名女性被诊断出患有乳腺癌，但如果癌症是局部的，并且在扩散到身体其他部位之前被发现，那么五年生存率为97%。因此，有助于早期发现和诊断乳腺癌的改进成像技术可以对妇女的保健产生深远的影响。该项目的研究重点是自体合成成像，该技术于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数学和计算方法旨在揭示乳腺癌筛查中断层合成的潜在变革益处，为医生提供更好的诊断信息。除了应用于乳腺癌筛查之外，断层合成在其全身实施中还可用于使用标准x射线和CT的许多其他应用，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物检测。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向临床应用的过渡。

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.