Binary Tomography Reconstruction From Few Projections With Level-set Regularization Methods For Bone Microstructure Study

Abstract

Discrete tomography refers to a class of reconstruction methods adapted to discrete-valued images. A number of methods have specifically been developed to address the binary case, when a two-phase object is considered. This problem may arise in different medical applications such as vascular or bone imaging where the goal is to reduce the number of projections. In this paper, we address the problem of binary image reconstruction for X-ray CT imaging from a small number of projections. We propose two new schemes based on level-set regularization. In the first approach, the binary tomography problem is formulated as a nonlinear inverse problem and regularized with Bounded Variation-Sobolev terms. A second level-set type method is investigated which includes the binary constraints in an augmented Lagrangian. For comparison, we consider a classical TV regularization method. The three schemes are applied to a simple disk image and to bone cross-sections images of various size without and with an additive Gaussian noise. The best binary reconstruction results are obtained with the TV algorithm for the simple disk image. Lower reconstruction errors are achieved with the level-set approaches methods for a more complex bone geometry and for the higher noise levels.