X-ray tomography is a reliable tool for determining density and three-dimensional (3D) structure of trabecuale bone . However, traditional reconstruction methods such as FDK require dense angular sampling in data acquisition phase leading to long measurement times. Acquiring less data using greater angular steps is an obvious way for speeding up the process. However, computing 3D reconstruction from such a sparsely sampled dataset is very sensitive to measurement noise and modelling errors. An automatic regularization method is proposed for robust reconstruction, based on enforcing sparsity in the three-dimensional shearlet transform domain. The inputs of the algorithm are the projection data and {\it a priori} known expected degree of sparsity, denoted $0<{\mathcal C}_{pr}\leq 1$. The number ${\mathcal C}_{pr}$ can be calibrated from a few dense-angle reconstructions and fixed. The morphology of the trabeculae bone is then analyzed using standard metrics. The proposed method is shown to outperform the baseline algorithm (FDK) in the case of sparsely collected data.

This presentation is part of Minisymposium “MS33 - Advances in reconstruction algorithms for computed tomography (4 parts)”
organized by: Gunay Dogan (Theiss Research, NIST) , Harbir Antil (George Mason University) , Elena Loli Piccolomini (Dept. Computer Science and Engineering, University of Bologna) , Samuli Siltanen (University of Helsinki) .

Authors:

Zenith Purisha (University of Helsinki)

Samuli Siltanen (University of Helsinki)

Keywords:

computed tomography, image reconstruction, image representation, inverse problems