Numerical solution of a nonlinear least squares problem in digital breast tomosynthesis

5th International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Landi, G.^1 ; Piccolomini, E Loli^1 ; Nagy, J.G.^2

Department of Mathematics, University of Bologna, Italy^1

Department of Mathematics and Computer Science, Emory University, United States^2

关键词: Digital breast tomosynthesis;    Digital tomosynthesis;    ILL-posed inverse problem;    Multiple projections;    Non-linear least squares;    Nonlinear least squares problems;    Numerical experiments;    Reconstruction process;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/657/1/012006/pdf
DOI  :  10.1088/1742-6596/657/1/012006

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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 (i.e., a set of 2D slices) of the object. In this paper we describe some mathematical models 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. A polyenergetic model helps to reduce beam hardening artifacts, but the disadvantage is that it requires solving a large-scale nonlinear ill-posed inverse problem. We formulate the image reconstruction process (i.e., the method to solve the ill-posed inverse problem) in a nonlinear least squares framework, and use a Levenberg-Marquardt scheme to solve it. Some implementation details are discussed, and numerical experiments are provided to illustrate the performance of the methods.