X-ray Diffraction Tomography: Image Filtering by Singular Value Decomposition and 1D Smoothing Whittaker–Eilers Methods

Abstract

Digital processing of the 2D noisy X-ray diffraction images (2D-XDI) of a single point defect in a Si(111) crystal, recorded at the level of dispersion of statistical Gaussian noise of the detector using filtering methods, such as singular value decomposition and 1D-line-by-line smoothing of test 2D-XDI, is carried out. The efficiency of digital filtering of 2D-XDI is evaluated and analyzed by means of the control parameter FOM (figure-of-merit) value of reconstruction of the displacement field function of a point defect of Coulomb type f_h(r – r₀), (h is the diffraction vector, r₀ is the radius-vector of the defect position in the sample). It is shown that the filtering technique using the singular value decomposition of 2D-XDI works much better than the 1D line-by-line smoothing method of 2D-XDI, which, apparently, as applied to our problem, requires further research for its improvement.