A nonlinear least squares method for solving the joint reconstruction and registration problem in digital breast tomosynthesis

Digital Breast Tomosynthesis (DBT) offers potential insight into the fine details of normal fibroglandular tissues and abnormal lesions, e.g., masses and micro-calcifications associated with breast cancer, by the production of a pseudo-3D image. In addition, it avoids the superposition, which is usually found in X-ray mammography, with a compa- rable radiation dose. Algorithms to aid the human observer process DBT data sets involve two key tasks: reconstruction and registration. In established medical image modalities these tasks are normally performed sequentially; the images are reconstructed and then registered. In this paper, we hypothesise that, for DBT in particular, combining the op- timisation processes of reconstruction and registration into a single algorithm will offer satisfactory for both tasks. Based on this hypothesis, we have devised a mathematical framework to combine these two tasks, and have implemented both affine and non-linear B-spline registration transformation models as plug-ins. By applying our algorithm to various simulated data, we demonstrate the success of our method in terms of both re- construction fidelity and in the registration accuracy of the recovered transformations