# COVID-19 Diagnosis by Extracting New Features from Lung CT Images Using Fractional Fourier Transform

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Database

#### 3.2. Pre-Processing

#### 3.3. Fractional Fourier Transform

#### 3.4. Feature Extraction and Selection

#### 3.5. Classification

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Showcases a selection of CT scans included in the dataset, demonstrating examples of both SARS-CoV-2-infected and non-infected patients.

**Figure 4.**This figure illustrates the contrast between the image prior to and following the implementation of pre-processing procedures. The raw image of the lung of a person infected with COVID-19 (

**A**); the image of the lung after pre-processing (

**B**).

**Figure 5.**FrFT is represented by two axes $\mathrm{u}{\mathrm{u}}^{\prime}$, and those axes are oriented by ϕ.

**Figure 7.**Classification based on average results (%) of fractional Fourier transform coefficients of imaginary, real, absolute value, and phase.

**Figure 8.**The average accuracy result (%) of KNN classification based on the number of K-neighbors for α = 0.8.

**Figure 9.**The average accuracy results (%) of the KNN classification based on distance type (Euclidean, Chebyshev, Mahalanobis, Minkowski) for α = 0.8.

**Figure 10.**KNN classification results (%) based on statistical method after applying 2D windowing and Euclidean distance with K-neighbor 1 (mean, median, minimum, maximum) for α = 0.8.

**Figure 11.**Average results (%) by the impacts of the number of features reduction. KNN Classifier (Green): Phase features, 1 number of neighbors, Euclidean distance with mean mathematical statistics (α = 0.8). SVM classifier (Blue): Absolute features, Polynomial kernel with median mathematical statistic (α = 0.7).

**Table 1.**SVM classification results based on SVM kernels with median statical method (RBF, Polynomial, Linear) for α = 0.7.

SVM | Kernels | ||
---|---|---|---|

RBF (%) | Linear (%) | Polynomial (%) | |

Accuracy | 99.59 | 92.53 | 99.86 |

Specificity | 99.18 | 89.04 | 99.69 |

Sensitivity | 100 | 100 | 100 |

Precision | 99.20 | 91.06 | 99.75 |

**Table 2.**SVM classification results based on statistical method after applying 2D windowing for Polynomial kernel with 200 features (mean, median, minimum, maximum) for α = 0.7.

Mathematical Statistic | Mean (%) | Median (%) | Minimum (%) | Maximum (%) |
---|---|---|---|---|

Accuracy | 96.41 | 99.90 | 98.30 | 95.88 |

Specificity | 92.75 | 99.83 | 96.58 | 92.69 |

Sensitivity | 100 | 100 | 100 | 100 |

Precision | 93.36 | 99.84 | 96.75 | 94.56 |

Model Used | Dataset | Results (%) | |
---|---|---|---|

Xu et al. [5] | DCNN-IPSCA | 1252 COVID-19 1229 Non-COVID-19 | ACC: 98.32 |

Peng et al. [17] | DeepDSR | 1252 COVID-19 1229 Non-COVID-19 | ACC: 98.94 |

Gupta et al. [22] | ResNet-50, and DenseNet-121. | 1252 COVID-19 1229 Non-COVID-19 | AUC: 85 |

Wu et al. [33] | ResNet50 | 1252 COVID-19 1229 Non-COVID-19 | AUC: 73.20 |

Ruano et al. [41] | End-To-End Deep learning | 1252 COVID-19 1229 Non-COVID-19 | ACC: 96.99 |

Proposed Method | FrFT | 1252 COVID-19 1229 Non-COVID-19 | SVM ACC: 99.90 KNN ACC: 99.84 |

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**MDPI and ACS Style**

Nokhostin, A.; Rashidi, S.
COVID-19 Diagnosis by Extracting New Features from Lung CT Images Using Fractional Fourier Transform. *Fractal Fract.* **2024**, *8*, 237.
https://doi.org/10.3390/fractalfract8040237

**AMA Style**

Nokhostin A, Rashidi S.
COVID-19 Diagnosis by Extracting New Features from Lung CT Images Using Fractional Fourier Transform. *Fractal and Fractional*. 2024; 8(4):237.
https://doi.org/10.3390/fractalfract8040237

**Chicago/Turabian Style**

Nokhostin, Ali, and Saeid Rashidi.
2024. "COVID-19 Diagnosis by Extracting New Features from Lung CT Images Using Fractional Fourier Transform" *Fractal and Fractional* 8, no. 4: 237.
https://doi.org/10.3390/fractalfract8040237