Development of a Spectral Reconstruction Algorithm for Breast Tomographic Imaging

This project focuses on the development of computational methods for tomographic breast image reconstruction. The mathematical models addressed in this project are difficult ill-posed inverse problems; computed solutions are very sensitive to errors in the data, and implementation for large scale 3-dimensional images is non-trivial. All previous breast tomographic image reconstruction algorithms use a simplified, but incorrect, assumption that the source x-ray beam is comprised of photons with a constant energy; that is, the x-ray beam is assumed to be mono-energetic. This project uses the physically correct, and hence more accurate, assumption that the x-ray beam is polyenergetic. The resulting mathematical model is nonlinear, providing great challenges to the development and analysis of mathematical models, as well as for the development of computational methods. However, as this project reveals, the non-linear model allows for image reconstruction with substantially fewer artifacts than the linear model. Moreover, the non-linear model can incorporate parameterizations to allow for explicit decomposition of the breast into distinct materials and for the introduction of advanced image acquisition techniques, such as tube voltage switching during acquisition of the projection set. This project involves a close collaboration with researchers in the Mathematics and Computer Science Department of Emory University.

Funding Agency: National Science Foundation

Grant Type: Computational Mathematics Standard Grant

Funding Period: 09/15/11-08/31/14

Figure 3
Improved image quality of a spherical insert in a breast phantom when reconstructed using the spectral reconstruction algorithm for breast tomosynthesis imaging.