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X-ray tomography is a reliable tool for determining the inner structure of 3Dobject with penetrating X-rays. However, traditional reconstruction methodssuch as FDK require dense angular sampling in the data acquisition phaseleading to long measurement times, especially in X-ray micro-tomography toobtain high resolution scans. Acquiring less data using greater angular stepsis an obvious way for speeding up the process and avoiding the need to savehuge data sets available memory. However, computing 3D reconstruction from sucha sparsely sampled dataset is very sensitive to measurement noise and modellingerrors. An automatic regularization method is proposed for robustreconstruction, based on enforcing sparsity in the three-dimensional shearlettransform domain. The inputs of the algorithm are the projection data and {\ita priori} known expected degree of sparsity, denoted $0<{\mathcal C}_{pr}\leq1$. The number ${\mathcal C}_{pr}$ can be calibrated from a few dense-anglereconstructions and fixed. Human subchondral bone samples were tested andmorphometric parameters of the bone reconstructions were then analyzed usingstandard metrics. The proposed method is shown to outperform the baselinealgorithm (FDK) in the case of sparsely collected data. The number of X-rayprojections can be reduced up to 10\% of the total amount while retaining thequality of the reconstruction images and of the morphometric paramaters.

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