X-ray tomography: how to evaluate the reconstruction quality?

Different reconstruction techniques are used to reconstruct the distribution of the physical characteristics, describing a sample under investigation, from a set of tomographic projections. We present a technique for the evaluation of the reconstruction quality. The technique is based on the comparison of two images (phantom and reconstructed image) by means of the correlation coefficient and of the mean square error between them. In parallel, the correlation coefficient and mean square error are calculated for the wavelet transforms of the phantom and reconstructed images. The scales for the wavelet transform are chosen in agreement with the major geometric parameters of the phantom. Then the correlation coefficient of the wavelet transform with the chosen scale yields an evaluation of the quality of the phantom parameters reconstruction. The accuracy of the parameters reconstruction is determined by the mean square error for the selected scale. The phantom used for the analysis is a medium with randomly distributed grains. The distribution is characterized by two parameters: grain size and grain density (average number of grains per unit area). The parameters are used as the scales for the wavelet transform calculation. We make a comparison of the Algebraic Reconstruction Technique (ART) and the Filtered Back Projection Algorithm.