An automatic regularization method: An application for 3D X-ray micro-CT reconstruction using sparse data

X-ray tomography is a reliable tool for determining the inner structure of 3D object with penetrating X-rays. However, traditional reconstruction methods such as FDK require dense angular sampling in the data acquisition phase leading to long measurement times, especially in X-ray micro-tomography to obtain high resolution scans. Acquiring less data using greater angular steps is an obvious way for speeding up the process and avoiding the need to save huge data sets available memory. 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. Human subchondral bone samples were tested and morphometric parameters of the bone reconstructions were then analyzed using standard metrics. The proposed method is shown to outperform the baseline algorithm (FDK) in the case of sparsely collected data. The number of X-ray projections can be reduced up to 10\% of the total amount while retaining the quality of the reconstruction images and of the morphometric paramaters.