X-ray data reconstruction from incomplete data sampling

Medina, K.G.; Rams, E.E.; Neder, R.B.

doi:10.1107/S1600576725010003

Figure 9
Metrics to choose the cut-off frequency. Three practical metrics have been defined that can be derived from the observed and reconstructed data. Cross-validation error was calculated for several instances of random sampling, and the average, 〈CVE〉, is reported (a). (b) As explained in the text, the overall normalized error (ONE) is determined between the final output of the iterative algorithm (g^(t)) and the original signal (y). The third metric, FS (c), is taken as the frequency value for which the power spectrum of the Fourier transform of the reconstructed signal reaches a given threshold. According to the MSE (d), the best reconstruction was attained with $[k_{\rm c} = 169]$ . Reconstructed signals for values around the MSE minimum are shown in the right column (e). 〈CVE〉 has a minimum at the neighboring point $[k_{\rm c} = 170]$ , leading to the second-best reconstructed signal near the absolute MSE minimum. The same $[k_{\rm c}]$ value is one of the two minima in the ONE figure of merit, while FS has a minimum value for $[k_{\rm c} = 174]$ , where the reconstruction is still visually close to the original signal despite not being near the cut-off frequency at which MSE reaches its minimum value.

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 58| Part 6| December 2025| Pages 2090-2104

https://doi.org/10.1107/S1600576725010003

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