Notwithstanding the discovery of vaccines for Covid-19, the virus's rapid spread continues due to the limited availability of vaccines, especially in poor and emerging countries. Therefore, the key issues in the present COVID-19 pandemic are the early identification of COVID-19, the cautious separation of infected cases at the lowest cost and curing the disease in the early stages. For that reason, the methodology adopted for this study is imaging tools, particularly computed tomography, which have been critical in diagnosing and treating the disease. A new method for detecting Covid-19 in X-rays and CT images has been presented based on the Scatter Wavelet Transform and Dense Deep Neural Network. The Scatter Wavelet Transform has been employed as a feature extractor, while the Dense Deep Neural Network is utilized as a binary classifier. An extensive experiment was carried out to evaluate the accuracy of the proposed method over three datasets: IEEE 80200, Kaggle, and Covid-19 X-ray image data Sets. The dataset used in the experimental part consists of 14142. The numbers of training and testing images are 8290 and 2810, respectively. The analysis of the result refers that the proposed methods achieved high accuracy of 98%. The proposed model results show an excellent outcome compared to other methods in the same domain, such as (DeTraC) CNN, which achieved only 93.1%, CNN, which achieved 94%, and stacked Multi-Resolution CovXNet, which achieved 97.4%. The accuracy of CapsNet reached 97.24%.

Ended in December 2019, a cluster of pneumonia cases with an unknown cause was linked to a seafood market in Wuhan, Hubei Province, China, and quickly becoming a pandemic [

Artificial Intelligence (AI) and related technologies are increasingly prevalent in healthcare and medical practice. It is relevant to visually-oriented specialty, such as radiography. This field has got particular attention; the reason is the wide use of x-ray examination, which is around two billion performed per year. AI techniques are also deeply employed in Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) to help the medical staff diagnose and treat diseases [

Real-time reverse-transcription polymerase chain reaction (RT-PCR), X-ray and CT are utilized to diagnose the Covid-19 to distinguish between infected and non-infected cases. The reports have found that RT-PCR has a lower sensitivity compering to CT of detect Covid-19 [

Ahmmed K. et al. (2020) begin with preprocessing the images of x-ray by converting them into grayscales and resize them into 100 × 100. The proposed Convolutional Neural Network (CNN) begins with 32 filters, then 64 filters, and max pooling filters. The result input is in a dense neural network for the classification of the image. The chest X-ray images were obtained from the Covid-19 Radiography Database, which was considered as a primary dataset in this work. This dataset contained 1341 normal and 219 Covid-19 patient’s images. The accuracy obtained from that model was 94% [

The study of Asmaa A. et al. (2020) validates Decompose, Transfer and Compose (DeTraC), a deep CNN for COVID-19 chest X-ray image classification. DeTraC can cope with anomalies in the picture dataset by employing a class decomposition process to investigate its class boundaries. The experimental results demonstrated DeTraC's capacity to detect COVID-19 cases from a large image dataset, and the accuracy gained for this approach was 93% [

This paper answers two questions; first, is a scattering wavelet an effecting feature to detect Covid-19 from x-ray images? While the second question is that scattering wavelet represents a discriminant feature that can build a classifier trained with a small dataset? This research aims to build a model that can detect the infected cases of Covid-19 from X-ray images.

The rest of the paper has been classified as follows: Section 2 discusses the wavelet scattering transform, while the dense deep neural network is debated in Section 3. The proposed technique is given in Section 4. Finally, the conclusion is presented in Section 5.

Since the capability of wavelets for multi-resolution image representation, the interest in using wavelet frames for image processing has grown over recent decades. The framelet transform is close to wavelet transform Framelet has two high-frequency filters, which produce more sub bands in decomposition. Convolutional structure of the windowed scattering transform means that each layer is captured from previous by applying wavelet modulus decomposition

The SWT was early presented by Mallat [

The SWT network consists of two layers without training and achieves similar performance to the convolutional network. The network generates a representation Φ that is invariant to rotation, translation, color discrimination and stability to small deformations. A scattering transform is the cascading of linear wavelet transform and modulus nonlinearity.

The image is filtered using the first wavelet transform W_{1}, _{3}x results from a final pooling. The pooling is average-pooling (AVG) or max-pooling defined by blocks of size.

The initial wavelet layer is described by the base wavelet ψ1 (u), a complex function with excellent image plane localization. This wavelet is scaled by 2j1 where j is an integer and rotated by

where

This wavelet transform is a filter on image x(u), and wavelet coefficients are computed by

The spatial variable

The index

Deep Learning (DL) has its origins in Artificial Intelligence and has emerged as a distinct and highly useful area in recent years [

The mathematical form of a fully connected network is

Here, σ is nonlinear, and the

while the weights w(l)ij of connection lines between node j in the layer number I and another node in layer

where

Relu usually has been used in deep dense neural networks. Relu function can be defined as follows:

Both the Relu function and its derivative are consistent. If the function receives any negative input, it returns 0; however, it returns that value if the input is positive. As a result, it produces an output from a range of 0 to infinity.

An active and accurate Covid-19 detection has been proposed based on the Scatter Wavelet Transform and DDNN. The SWT has been employed as a feature extractor, while the DDNN is utilized as a binary classifier. Firstly, it extracts all scattering wavelet feature sets from an image pattern. The scattering wavelet list of each image consists of 7812 features saved inside a list. The system converts each x-ray image to its scattering wavelet counterpart.

The converted images or the list of scattering wavelet images are divided into training and testing set of 80% and 20%, respectively. The values produced from the scattering wavelet transformation process are over 1, so these values have to be normalized and converted in decimal format between 0 and 1 to be accepted by DDNN. The DDNN classifier consists of five layers. First, the input layer that is flattening the input list of 7812 features of each x-ray image; then three hidden layers with Relu functions consist of 256,128,64 neurons, respectively; lastly, the output layer that has one neuron with sigmoid activation function, which yields wither normal lung or infected one. DDNN architecture of the proposed system is apparent in

This Deep Dense Neural Classifier uses Adam that is short of adaptive moment estimation, a momentum-based optimizer. The loss function used is binary cross entropy. The binary classification problems give output in the form of probability. Binary cross entropy is usually the optimizer of choice.

To test the proposed framework, this research has used three datasets for training, testing and evaluating the proposed method that has been developed to detect Covid-19 infections intelligently. The existing datasets have the disequilibrium issue. This issue is handled by class weighting within the training process.

Dataset | Number of images | ||
---|---|---|---|

Normal | Covid | ||

IEEE 80200 | Training | 69 | 108 |

Testing | 45 | ||

Kaggle | Training | 8157 | 2889 |

Testing | 2762 | ||

COVID-19 X-ray Image Data Sets | Training | 64 | 45 |

Testing | 3 |

The datasets vary between big datasets as Kaggle [

Five metrics that measure system efficiency in this paper are: accuracy, precision, recall, sensitivity and specificity. These five metrics are derived from four parameters: true positive (TP), true negative (TN), false positive (FP) and false-negative (FN). The formulas of these metrics are in equations from 16 to 19:

The features were extracted using scattering wavelet transform, while the proposed system used DDNN as a binary classifier to classify the input x-ray images to either be detected with Covid-19 or not. The DDNN is a fully connected deep network that use a linear operation where every input is connected to every output by a wight. The system is trained using adaptive moment learning rate (ADAM) with epochs between 60 and 100 that is using the early stop in keras library that makes the training process stops when the model gets the best accuracy.

The results show that using scattering wavelet feature with deep dense neural networks classifier achieved high performance. The performance of the proposed model is clear for both small datasets like the third dataset of Covid-19 and larger ones like Kaggle and IEEE 8023. From

Dataset | Precision | Recall | Accuracy | Specificity | Sensitivity | Support | |
---|---|---|---|---|---|---|---|

IEEE8023 | |||||||

Kaggle | |||||||

Covid-19 Dataset | |||||||

In the discussion section, the proposed model has been compared with previous related works; this is shown in

The proposed model tested with the mentioned datasets. The resulted accuracy values are answering the two mentioned research questions in the introduction section. First, is scattering wavelet is an efficient? The accuracy values were achieved in the tests indicate that scattering wavelet transform is an efficient enough to train covid-19 detection model.

The second research question was whether the scattering wavelet efficient as a discriminant feature to build the covid-19 detection system with a small training set?

The system also tested with mentioned second dataset and the accuracy was high and stable with 97%.

Reference | Total Image | Normal | Covid | Method | Accuracy |
---|---|---|---|---|---|

Article [ |
625 | 500 | 125 | DarkNet | 98.0% |

Article [ |
2971 | 1341 | 285 | CNN | 94.0% |

Article [ |
196 | 80 | 105 | (DeTraC) CNN | 93.1% |

Article [ |
610 | 305 | 305 | stacked MultiResolution CovXNet | 97.4% |

Article [ |
1281 | 1050 | 231 | CapsNet | 97.24% |

Article [ |
3400 | 3000 | 400 | CheXnet | 96% |

Article [ |
1531 | 1431 | 100 | CNN | 96% |

Article [ |
889 | 408 | 526 | Merge of (Densenet201,Resnet50v2, inceptionv3) | 91% |

Article [ |
3141 | 2800 | 341 | Merge of (Resnet50, Resnet101, Resnet152, inception v3,inception-Resnt v2) | 98% |

Proposed model | 177 | 108 | 69 | Scattering wavelet and deep neural classifier | 98.0% |

Because of the vast number of deaths caused by the coronavirus pandemic, healthcare services in every country have been stretched to their limits. COVID-19 can be detected early and treated more quickly, simpler and less expensively will save lives and relieve the pressure on medical providers. The image processing techniques and artificial intelligence to X-ray images will play a major role in identifying COVID-19. This research has crafted an intelligent framework for identifying COVID-19 with high accuracy and minimal complexity. The present research aims to investigate the use of scattering wavelet as a discriminative feature to detect Covid-19 from x-ray images supported by deep learning technique. The proposed system was applied to three different datasets that are varying in size. The first dataset consists of 231 pictures, the second dataset contains 13808 x-ray pictures, and the third dataset consists of 112 pictures. The proposed system shows a stable efficiency even with a small dataset. The results insisted that the scattering wavelet is efficient in providing discriminative features about the internal patterns of images even in the case of small dataset availability. Moreover, the proposed work employed the effectiveness of deep learning of classification.

These training and testing images represent all of the images from the previous experiments. The results of the present study are compared to other methods in the same domain. It is identified that the proposed method has achieved an accuracy of 98% when compared to (DeTraC) CNN, which achieved only 93.1%, CNN, which achieved 94% and stacked MultiResolution CovXNet, which achieved 97.4%. The accuracy of CapsNet reached 97.24%. For future studies, the area of detecting Covid-19 from x-ray images needs much more patient datasets, well organized, balanced and standard, because current datasets have issues like unbalancing between classes or some mistakes like normal cases images stored accidentally in Covid-19 patient classes and vice versa.