# Reconstruction of PET Images Using Cross-Entropy and Field of Experts

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. ML-EM Algorithm

#### 2.2. Cross-Entropy

#### 2.3. Field of Experts Model

#### 2.4. Proposed Objective Function

## 3. Results

#### Simulated Data

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The $5\times 5$ filters obtained by training the oroduct-of-experts model on positron emission tomography (PET) images database. The colors in each frame are proportional to the magnitude of the filter coefficient, using a gray scale.

**Figure 2.**Cylindrical software phantom: (

**a**) ground truth; (

**b**) simulated sinogram data at 30 M counts; and (

**c**) reconstruction with expectation maximization (EM).

**Figure 3.**Cylindrical software phantom: (

**a**) Input sinogram; (

**b**) low count reconstruction with EM; (

**c**) low count reconstruction with CP; and (

**d**) low count reconstruction with the proposed method.

**Figure 4.**Profiles of the different methods with the cylindrical software phantom. Each row shows the same hole, and each column the same method. The maximum of each surface is indicated next to it.

**Figure 5.**Slices of the Digimouse software phantom: ground truth (

**a**,

**e**); low count reconstruction with EM (

**b**,

**f**); low count reconstruction with CP (

**c**,

**g**); and (

**d**,

**h**) low count reconstruction with the proposed method. In (

**a**), the arrow indicates a lesion.

Method | CR |
---|---|

EM | 0.577 |

CP | 0.541 |

Proposed | 0.695 |

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**MDPI and ACS Style**

Mejia, J.; Ochoa, A.; Mederos, B.
Reconstruction of PET Images Using Cross-Entropy and Field of Experts. *Entropy* **2019**, *21*, 83.
https://doi.org/10.3390/e21010083

**AMA Style**

Mejia J, Ochoa A, Mederos B.
Reconstruction of PET Images Using Cross-Entropy and Field of Experts. *Entropy*. 2019; 21(1):83.
https://doi.org/10.3390/e21010083

**Chicago/Turabian Style**

Mejia, Jose, Alberto Ochoa, and Boris Mederos.
2019. "Reconstruction of PET Images Using Cross-Entropy and Field of Experts" *Entropy* 21, no. 1: 83.
https://doi.org/10.3390/e21010083