Correction to: Deep learning-based PET image denoising and reconstruction: a review

Correction to: Radiological Physics and Technology (2024) 17:24–46 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:

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

Correct version:

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

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

Correct version:

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

The original article has been corrected.