Digital tomosynthesis imaging is becoming increasingly significant in a variety of medical imaging applications. Tomosynthesis imaging involves the acquisition of a series of projection images over a limited angular range, and reconstruction results in a pseudo-3D representation of the imaged object. In breast cancer imaging, tomosynthesis is a viable alternative to standard mammography; however, current algorithms for image reconstruction do not take into account the polyenergetic nature of the x-ray source beam entering the object. This results in inaccuracies in the reconstruction, making quantitative analysis challenging and allowing for beam hardening artifacts. We develop a mathematical framework based on a polyenergetic model and develop statistically based iterative methods for polyenergetic tomosynthesis reconstruction for breast imaging. Large-scale problems pose some computational challenges, and implementation concerns are addressed.
