Correction to: Radiological Physics and Technology (2024) 17:24–46 https://doi.org/10.1007/s12194-024-00780-3


In the original PDF of this article, the formula 5 was published with extraneous text as “* 20c”.


Incorrect version:

$$* 20cL\left({\varvec{y}}|{\varvec{x}}\right)=-{\text{log}}P\left({\varvec{y}}|{\varvec{x}}\right)=C-{\sum }_{i=1}^{I}\left\{{y}_{i}{\text{log}}\left({\sum }_{j=1}^{J}{a}_{\mathit{ij}}{x}_{j}+{\overline{b} }_{i}\right)-\left({\sum }_{j=1}^{J}{a}_{ij}{x}_{j}+{\overline{b} }_{i}\right)\right\},$$
(5)

Correct version:

$$L\left({\varvec{y}}|{\varvec{x}}\right)=-{\text{log}}P\left({\varvec{y}}|{\varvec{x}}\right)=C-{\sum }_{i=1}^{I}\left\{{y}_{i}{\text{log}}\left({\sum }_{j=1}^{J}{a}_{\mathit{ij}}{x}_{j}+{\overline{b} }_{i}\right)-\left({\sum }_{j=1}^{J}{a}_{ij}{x}_{j}+{\overline{b} }_{i}\right)\right\},$$
(5)

The HTML version was unaffected.


In this article the formula 13 was incorrectly published with a minus (-) symbol in the denominator instead of plus ( +) symbol.


Incorrect version:

$${x}_{j}^{\left(k+1\right)}=\frac{{x}_{j}^{\left(k\right)}}{\sum_{i=1}^{I}{a}_{ij}-\beta {\left.\frac{\partial U\left({\varvec{x}}\right)}{\partial {x}_{j}}\right|}_{{\varvec{x}}={{\varvec{x}}}^{(k)}}}{\sum }_{i=1}^{I}\frac{{a}_{ij}{y}_{i}}{{\sum }_{{j}^{\prime}=1}^{J}{a}_{i{j}^{\prime}}{x}_{{j}^{\prime}}^{\left(k\right)}+{\overline{b} }_{i}}.$$
(13)

Correct version:

$${x}_{j}^{\left(k+1\right)}=\frac{{x}_{j}^{\left(k\right)}}{\sum_{i=1}^{I}{a}_{ij}+\beta {\left.\frac{\partial U\left({\varvec{x}}\right)}{\partial {x}_{j}}\right|}_{{\varvec{x}}={{\varvec{x}}}^{(k)}}}{\sum }_{i=1}^{I}\frac{{a}_{ij}{y}_{i}}{{\sum }_{{j}^{\prime}=1}^{J}{a}_{i{j}^{\prime}}{x}_{{j}^{\prime}}^{\left(k\right)}+{\overline{b} }_{i}}.$$
(13)

The original article has been corrected.