On the Theory of Reducing the Level of Statistical Noise and Filtering of 2D Images of Diffraction Tomography

According to the diffraction tomography data, the efficiency of minimization algorithms used to reconstruct the displacement field of a defect in a crystal depends on the presence of a noise component and implies preliminary use of noise filtering algorithms. The quality of projection image filtering has been estimated using the root-mean-square deviations of the intensity of a denoised image from the intensity of the initial noiseless image in a fixed rectangular neighborhood of the defect under study and beyond it. A comparison of these quantities, calculated after application of different noise filtering algorithms, has shown that their minimum values are obtained simultaneously using a guided image filter. The 3D reconstruction based on the projection images denoised in this way has significantly improved the quality of reconstructing the defect displacement field as compared with the results based on noisy unfiltered images.