Multispectral Tomosynthesis Imaging: Mathematical Models, Algorithms and Software

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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.