# Classification of Covid-19 Coronavirus, Pneumonia and Healthy Lungs in CT Scans Using Q-Deformed Entropy and Deep Learning Features

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## Abstract

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## 1. Introduction

## 2. Related Work

- (1)
- By achieving efficient classification results under limited computational resources with the use of fewer parameters on the collected 321 chest CT scans, we have shown that the proposed approach could effectively improve the performance of classifying lungs in CT scans.
- (2)
- The new proposed Q-deformed entropy features which are used as new texture extracted features for image classification tasks.
- (3)
- The proposed nine layers fully convolutional network architecture which is used to extract the deep features from lungs’ CT scans.

## 3. Materials and Methods

#### 3.1. Data Collection

#### 3.2. CT Lung Scan Preprocessing

Algorithm 1: Pseudo-code for CT lung scans preprocessing. |

Input: Input image I(n,m) |

Output: Output image K(n,m) |

begin |

Adjust image intensity values |

Convert the image into a binary image(B) |

For all I pixels: |

IF the grayscale value < the image Mean, |

THEN, the pixel value = 0 |

ELSE the pixel grayscale value = 255 |

End IF |

End For |

Remove small objects from binary image, and Fill image regions and holes |

Produce the output image(K) |

For each Input image I do |

For i = 1 to n do |

For j = 1 to m do |

Multiply each element in I(i,j) by the corresponding element |

in B(i,j) and return the output image(K) |

End For |

End For |

End For |

#### 3.3. Q-Deformed Entropy Feature Extraction (QDE)

Algorithm 2: Pseudo-code for the proposed Q-deformed entropy feature extraction (QDE) algorithm. |

Initialization: I = Input image, 0 < q < 3 |

For each Input image I do |

(b1, b2, …, bn) $\leftarrow $ divide I into n blocks of size m x m pixels |

For i = 1 to n do |

QDE in Equation (5), where i denotes the ith block of m x m |

dimension |

End For |

QDE ← I = (1, 2, …n) // QDE Features of all (n) blocks |

End For |

#### 3.4. Deep Learning for Feature Extraction

- $Con{v}_{1}$ (filters of size 3 × 3, stride of 1, padding of 1, and kernels of 16) are applied:$$Con{v}_{width,height}=\frac{256-3+\left(2\times 1\right)}{1}+1=256.$$For the feature maps, we have 256 × 256 × 16 = 1,048,576 neurons.
- $MaxPoolin{g}_{1}$ is equal to the previous feature maps divided by the stride number:$$MaxPoolin{g}_{1}=\frac{256}{2}=128.$$For the feature maps, we have 128 × 128 × 16 = 262,144 neurons in the feature map of the first max pooling layer.
- $Con{v}_{2}$ (filters of size 5 × 5, a stride of 1, padding of 2 and kernels of 32) are applied:$$Con{v}_{width,height}=\frac{128-5+\left(2\times 2\right)}{1}+1=128.$$For the feature maps, there are 128 × 128 × 32 = 524,288 neurons.
- $MaxPoolin{g}_{2}$ is equal to the previous feature maps divided by the stride number:$$MaxPoolin{g}_{2}=\frac{128}{2}=64.$$For the feature maps, we have 64 × 64 × 32 = 131,072 neurons.
- $Con{v}_{3}$ (filters of size 5 × 5, a stride of 1, padding of 2 and kernels of 64) are applied:$$Con{v}_{width,height}=\frac{64-5+\left(2\times 2\right)}{1}+1=64.$$For the feature maps, we have 64 × 64 × 64 = 262,144 neurons in the feature map of the third convolution layer.
- $MaxPoolin{g}_{3}$ is equal to the previous feature maps divided by the stride number:$$MaxPoolin{g}_{3}=\frac{64}{2}=32.$$For the feature maps, we have 32 × 32 × 64 = 65,536 neurons.
- $Con{v}_{4}$ (convolutional filters of size 7 × 7, a stride of 1, padding of 3 and kernels of 128) are applied:$$Con{v}_{width,height}=\frac{32-7+\left(2\times 3\right)}{1}+1=32.$$For the feature maps, we have 32 × 32 × 128 = 131,072 neurons.
- The fully connected (FC) layer determines the class scores by combining all features which are produced and learned by the previous layers to produce a feature map of size 1 × 1 × 3, that is equal to the number of classes in the dataset. The input size of the FC layer is equal to 131,072 that is produced by $Con{v}_{4}$.

#### 3.5. LSTM Neural Network Classifier

_{t}is the current input, C

_{t}and C

_{t−1}denote the new updated cell state and cell state from last LSTM unit, respectively, h

_{t}and h

_{t−1}represent the current output and the output of the last LSTM unit, respectively [37]. The forget gate uses the previous LSTM’s output h

_{t−1}and the current input x

_{t}to produce a vector of numbers, ranging from 0 to 1, corresponding to each value in C

_{t−1}to decide which information should be kept and which should be discarded from C

_{t−1}. The forget gate is given by [39]:

_{f}and b

_{f}are the weighted matrices, and the bias of the forget gate of LSTM, respectively.

_{t}and the output of the previous LSTM h

_{t−1}are important and allow them to pass to the next gate after normalizing them into a new range between −1 and 1 to regulate the LSTM network by using Equations (10)–(12), as shown in the following [40]:

_{t}and N

_{t}are the outputs of the sigmoid function and the tanh function, respectively. W

_{i}and bi are the weighted matrices and the bias of the input gate of LSTM, respectively. Then, the previous cell state C

_{t−1}is updated by multiplying it with the forget gate output to drop values in the cell state if the corresponding values in the forget gate output are close to 0 as given in Equation (13) [32,37].

_{t}is the current cell state of LSTM network.

_{t}is updated by adding the output of the input gate, as given in Equation (14) [22]:

_{t}after passing through a tanh function and the previous output h

_{t−1}after passing through a sigmoid function, as given in Equation (15) and Equation (16):

## 4. Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Computed tomography (CT) slices of lung in axial view: (

**a**) infected lung with COVID-19, and (

**b**) infected lung with pneumonia.

**Figure 3.**An example of lung boundary identification: (

**a**) original CT slice, and (

**b**) segmented CT slice.

**Figure 4.**Architecture of the convolutional neural network (CNN) as a feature extractor with four convolutional layers, three pooling layers and one fully connected layer.

**Figure 6.**CT scans of the lung from the collected dataset: (

**a**) healthy lung, (

**b**) COVID-19 infection and (

**c**) pneumonia infection.

**Figure 7.**The images of learned weights of the CNN layers: (

**A**) Conv1 (1 × 16), (

**B**) Conv2 (1 × 32), (

**C**) Conv3 (1 × 46), and (

**D**) Conv4 (1 × 128).

Layer Name | Kernel Size | Feature Map |
---|---|---|

Input layer | (256 × 256) | |

Conv1 | (3 × 3) | (256 × 256 × 16) |

Max. Pooling1 | (2 × 2) | (128 × 128 × 16) |

Conv2 | (5 × 5) | (128 × 128 × 32) |

Max. Pooling2 | (2 × 2) | (64 × 64 × 32) |

Conv3 | (5 × 5) | (64 × 64 × 64) |

Max. Pooling3 | (2 × 2) | (32 × 32 × 64) |

Conv4 | (7 × 7) | (32 × 32 × 128) |

FC | (1 × 3) | (1 × 3) |

**Table 2.**Comparisons of QDE (Q-deformed entropy), deep features (DF) and the proposed QDE–DF using LSTM (long short-term memory).

Method | Accuracy 100% | TP 100% COVID-19 | TP 100% Healthy | TP 100% Pneumonia |
---|---|---|---|---|

QDE | 97.50 | 95.70 | 100 | 96.80 |

DF | 98 | 97.40 | 100 | 96.80 |

QDE–DF | 99.68 | 100 | 100 | 98.90 |

Method | Accuracy 100% | TP 100% COVID-19 | TP 100% Healthy | TP 100% Pneumonia |
---|---|---|---|---|

Linear SVM | 96.20 | 94.90 | 98.10 | 95.80 |

KNN | 95.30 | 93.20 | 97.20 | 95.80 |

Logistic Regression | 97.20 | 96.60 | 98.10 | 96.80 |

LSTM | 99.68 | 100 | 100 | 98.90 |

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## Share and Cite

**MDPI and ACS Style**

Hasan, A.M.; AL-Jawad, M.M.; Jalab, H.A.; Shaiba, H.; Ibrahim, R.W.; AL-Shamasneh, A.R.
Classification of Covid-19 Coronavirus, Pneumonia and Healthy Lungs in CT Scans Using Q-Deformed Entropy and Deep Learning Features. *Entropy* **2020**, *22*, 517.
https://doi.org/10.3390/e22050517

**AMA Style**

Hasan AM, AL-Jawad MM, Jalab HA, Shaiba H, Ibrahim RW, AL-Shamasneh AR.
Classification of Covid-19 Coronavirus, Pneumonia and Healthy Lungs in CT Scans Using Q-Deformed Entropy and Deep Learning Features. *Entropy*. 2020; 22(5):517.
https://doi.org/10.3390/e22050517

**Chicago/Turabian Style**

Hasan, Ali M., Mohammed M. AL-Jawad, Hamid A. Jalab, Hadil Shaiba, Rabha W. Ibrahim, and Ala’a R. AL-Shamasneh.
2020. "Classification of Covid-19 Coronavirus, Pneumonia and Healthy Lungs in CT Scans Using Q-Deformed Entropy and Deep Learning Features" *Entropy* 22, no. 5: 517.
https://doi.org/10.3390/e22050517