Binary tomography reconstruction from few projections with Total Variation regularization for bone microstructure studies

Discrete tomography refers to a class of reconstruction methods adapted to discrete-valued images. Many different approaches have been investigated to address the binary case, when a two-phase object is considered. This reconstruction problem is very important in medical or material applications where it is crucial 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 a TV (Total Variation) regularization approach and compare the results obtained with or without an additional box convex constraint. The schemes are applied to a simple disk image and to more complex bone cross-sections for various noise levels. The minimization of the regularization functional is performed with the state-of-the-art ADMM (Alternate Direction Minimization Method) algorithm. The methods perform equally well on a simple disk image. The additional box convex constraints improves the reconstruction results for complex structures with fine details.