Iterative Breast Tomosynthesis Image Reconstruction

Abstract

In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of different incident angles in order to reconstruct a pseudo-3D representation of the object. In this paper we discuss a mathematical model for polyenergetic digital breast tomosynthesis image reconstruction that explicitly takes into account various materials composing the object and the polyenergetic nature of the x-ray beam. Our model allows for computing weight fractions of the individual materials that make up the object, which can then be used to reconstruct pseudo-3D images. The reconstruction process requires solving a large-scale inverse problem, which is done with a gradient descent iteration. Regularization is enforced by truncating the iteration. The mathematical model is described in detail, as is an efficient approach to compute the gradient of the objective function. The effectiveness of our approach is illustrated with real data taken of an object with known materials that simulates an actual breast.