Numerical Algorithms for Polyenergetic Digital Breast Tomosynthesis Reconstruction

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, which, after reconstruction, results in a pseudo-three-dimensional (3D) representation of the imaged object. The partial separation of features in the third dimension improves the visibility of lesions of interest by reducing the effect of the superimposition of tissues. 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. In this paper, we develop a mathematical framework based on a polyenergetic model and develop statistically based iterative methods for digital tomosynthesis reconstruction for breast imaging. By applying our algorithms to simulated data, we illustrate the success of our methods in suppressing beam hardening artifacts and improving the overall quality of the reconstruction.