# Correction to: Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners

The Original Article was published on 19 June 2020

## 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

1. 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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Correspondence to Nikos Efthimiou.

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