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Abstract <p>Digital processing of the 2D noisy X-ray diffraction images (2D-XDI) of a single point defect in a&#xa0;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 <i>f</i><sub><b>h</b></sub>(<b>r</b>&#xa0;– <b>r</b><sub>0</sub>), (<b>h</b> is the diffraction vector, <b>r</b><sub>0</sub> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • F. N. Chukhovskii,
  • P. V. Konarev,
  • V. V. Volkov

摘要

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 fh(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.