Iterative Breast Tomosynthesis Image Reconstruction

In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of di↵erent 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 to-mosynthesis 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 ecient approach to compute the gradient of the objective function. The e↵ectiveness of our approach is illustrated with real data taken of an object with known materials that simulates an actual breast. 1. Introduction. Image reconstruction algorithms used, for example, in computed tomography (CT), require solving large-scale inverse problems of the form