Correction to: EJNMMI Phys (2020) 7:42 https://doi.org/10.1186/s40658-020-00309-8
Following publication of the original article [1], two typographical errors were found by the authors in formulas 6 of the main text and 19 in the appendix. The original and correct versions of the equations are given below:
Original formula 6: \(F_{D}(d;\lambda) = \left(\frac{1 - \text{sgn}(d)}{2} - \text{sgn}(d) (\cosh{(\lambda(T - \left|d \right|))} - 1)\, \text{csch}\left(\frac{T\lambda}{2}\right)^{2}\right) \Big/ 4\).
Correct formula 6: \(F_{D}(d;\lambda) = \frac{1 + \text{sgn}(d)}{2} - \text{sgn}(d) (\cosh{(\lambda(T - \left|d \right|))} - 1)\, \text{csch}\left(\frac{T\lambda}{2}\right)^{2} \Big/ 4\).
Original formula 19: \(H=exp(2d\lambda)(E+F)\).
Correct formula 19: \(H=exp(2d\lambda)(-E+F)\).
The original article [1] has been corrected.
Reference
Efthimiou N, Thielemans K, Emond E, et al. Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners. EJNMMI Phys. 2020;7:42. https://doi.org/10.1186/s40658-020-00309-8.
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Efthimiou, N., Thielemans, K., Emond, E. et al. Correction to: Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners. EJNMMI Phys 9, 14 (2022). https://doi.org/10.1186/s40658-022-00441-7
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DOI: https://doi.org/10.1186/s40658-022-00441-7