Covid-19 is a disease that affects the respiratory system of the human body, and detecting this disease is a complex and one of the main challenges. This work proposed a technique for detection of COVID-19 by integrating multifocal images based on wavelet transduction. In order to improve the detection of COVID-19, Magnet resonant imagery (MRI) and computation tomography (CT) have been used. The multifocal image is included in order to support the diagnosis made by the clinicians. The seven-wave based algorithm bior2.2, coif2, db2, dmey, rbio2.2, sym4 and haar, respectively, was used to achieve a range of results. This approach effectively combines the data obtained from CT and MRI scans to produce a merged image that improves disease diagnosis efficiency by using MATLAB to determine the efficiency of the algorithm. The signal-to-noise ratio (PSNR) and the entropy factor are used to measure the image fusion efficiency. The statistical analysis of the final images demonstrated the superiority of the image attributes over both the CT image and the MRI.
Research Article
Detection of COVID-19 using wavelet transform
https://doi.org/10.21203/rs.3.rs-2113970/v1
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Covid-19 detection
Magnetism Resonant Imaging (MRI)
Calculated Tomography (CT)
Discrete Wavelet Transform (DWT)
Fusing
The virus that causes severe acute respiratory syndrome (Corona), which has been labeled The Health Organization has declared a worldwide problem, is known as Covid-19. Soft tissue information is provided by magnetic resonance imaging (MRI), while bone features are revealed by computed tomography (CT). Image fusion is a method of combining a large chrominance image with a limited spectral information to produce the highest multitemporal image that contains both multispectral image with large location data and color information (Udomhunsakul, and Wongsita 2004). This method is used to optimize images data and enhance image quality. It is highly beneficial to detect disorders and associated diagnoses such that appropriate treatment can be given. Previous studies focused on detecting COVID-19 using different techniques such as: random vector functional link (RVFL) network (Hazarika and Gupta 2020), transfer learning (Pahar et al. 2022), Deeper sound encoders and wavelet scattering features retrieved from limited image features (Despotovic et al. 2021), Discrete wavelet transform (DWT) and empirical mode deconstruction (EMD)( Erdoğan and Narin 2021), and a support vector machine (SVM) classifier and DWT (Sarhan 2021).
A. Transform of Wavelets
Wavelet transformations are used to breakdown a signal into levels, each of which corresponds to a lower focal wave and greater frequency ranges and resolution. Continuous and discrete conversions are the two basic types of conversions. DWT, which continuously adds a 2-channel filter banks on the lower range with down sampling (initially the original signal). The wavelet form is thus the Minimal of wavelet-based CT and MRI image integration which convert two low-resolution pass bands and the increased bands produced at every step into two high-resolution passage band. This transformation is non-redundant and invertible. The DWT is a space - time reduction that can be used to analyze multi - resolution images. The DWT's primary principle describes signals as a combination of wavelet. The wavelet decomposition is (Parmar et al. 2012):
\(f\) (t) =\(\sum _{m,n}{c}_{m,n} \psi\) m.n(t) (1)
Where \(f\)(t) is a discrete signal, \(\psi\) m.n(t) =\({2}^{\frac{-m}{2}}\psi [{2}^{-m}t-n]\) and m and n are integers.
There are highly specific values of \(\psi\) like that \(\psi m,n\left(\text{t}\right)\) is an axial foundation, allowing parameters of the wavelet decomposition to be calculated internally:
$${C}_{m,n}=\left(f ,{ \psi }_{m,n}\right)=\int { \psi }_{m,n}\left(t\right)f\left(t\right)dt$$
2
A scaling function\({{\phi }}_{\text{m},\text{n}}\), as well as its dilated and translated form, are required to build a multiresolution analysis described in Eq. (3):
$${{\phi }}_{\text{m},\text{n}}\left(\text{t}\right)={2}^{-\frac{\text{m}}{2}} {\phi }\left[{2}^{-\text{m}} \text{t}-\text{n}\right]$$
3
Depending on the characteristics of the covered level space and by expanding it into the appropriate areas, the f(t) can be decomposed into its finer components and features of varied sizes. As a result, extra coefficients am,n are necessary at each scale to obtain such decomposition directly. At every level, the coefficients am, n and am−1,n define the estimates of the functional \(f\)(t) for resolutions of \({2}^{m}\)and \({2}^{m-1}\), respectfully, whereas the coefficient \({C}_{m,n}\)and reflect the information loss when switching between approximations. To get am,n at each level and location, it is possible to extract the wavelet and approximation coefficients as(Parmar et al. 2012):
\({a}_{m,n}\) =\(\sum _{k}h\) \({2}^{(2-k)}{a}_{m-1,k}\) (4)
\({C}_{m,n}=\sum _{k}g\) \({2}^{(2-k)}{a}_{m-1,k}\) (5)
Where \({g}_{n}\), \({ h}_{n}\) are higher and lower passing FIR filter that is linked to \({ h}_{n}\). The analytical filter could be chosen from one biological package that has a corresponding set of synthesized filters\(\tilde{h}\) and \(\tilde{g }\) in order to rebuild the original signals. The signal is excellently reconstructed using these synthesis filters:
\({\text{a}}_{\text{m}-1,\text{l}}\left(\text{f}\right)=\sum _{\text{n}}[{ \tilde{h} 2}^{\left(2-l\right)}{a}_{m-n }\left(\text{f}\right)+\) \(\tilde{g }{2}^{\left(2-l\right)}{a}_{m-n}\left(\text{f}\right)]\) (6)
Filtering and down sampling are used to perform Eqs. (4–6), on the other hand, is initial up sampling and filtering.
B. Image Fusing using Wavelet Transform
in DWT, the original images of source and target images are decomposed. This is demonstrated by the representation of many states, each of which represents a distinct parameter (horizontal, vertical, diagonal, and zero). The various black squares related to each level of decomposition are associated with the coefficient of the identical spatial structure of the image in each original image, which has the same pixel coordinates in the original image. Inverse discrete wavelet transform (IDWT) creates the final fused image after obtaining a fused multi-scale (Mane and Sawant 2013). Figure 1 shows the integration of images into wavelet transforms at the second level.
A wavelet transformation fusion is a type of image fusion that uses to modified images. It incorporates all methods for merging in the field of conversion, transforming images according to a specified merging criteria before returning to the waveform. As a result, the wavelet transformation fusion was more explicitly established by examining the collected MRI\({ I}_{1}\) (x, y) and CT \({I}_{2}\) (x, y) images. After calculating the reversed wavelet translation, the combined image I (x, y) is reconstructed (Parmar et al. 2012):
I(x, y) =\({{\omega }}^{-1}\left({\phi }\left({\omega }\left({\text{I}}_{1}\left(\text{x}, \text{y}\right)\right), {\omega }\left({\text{I}}_{2}\left(\text{x}, \text{y}\right)\right)\right)\right) \left(7\right)\)
C. Wavelet Analysis
Wavelet analysis can be useful for discovering data properties such as trends, pauses, higher derived break, and identity that are missed by conventional signal analysis approaches. Wavelet analysis enables reduce or remove noise from the signal without inflicting real damage. Wavelet analysis is therefore essential when dealing with critical information, such as medical imaging, (Dwith et al. 2013). The fundamental algorithm separates the input CT and images MRI into images of secondary decay breakdown at the second level, as shown in Figure (2).
To approximate the CT and MRI images, at every level, low-pass (L) and high-pass (H) filtration are used to deconstruct them into rows and columns. Low-Low (LL) and Low-High (LH), High-Low (HL), and High-High (HH) coefficients are described in depth. Smooth filters or low pass filters are related with the scaling function, while high-pass filtering is associated with the wavelet function (Sapkal and Kulkarni 2012).
In the current study, the infected image data obtained by MRI and CT were inserted as a matrix of pixels in two dimensions of the matrix using Matlab R2016. Images are shown in grayscale or different brightness, and data is saved in Matlab. Normally, these images can be described by providing a big matrix with entrance points ranging from 0 to 255. This method involves multiple steps.
1- First step:
The source images (MRI and CT scans) of the sample are processed in this step to improve the contrast and brightness before being downsized to 128 * 128.
2- Second step:
The MRI and CT images are subjected to the wavelet transformation, and for the best outcomes, they are mixed individually using various wavelet filters (Coiflets, Daubechies, haar, etc.).
3- Third step:
By integrating MRI and CT, wavelet approaches are applied to get the best results possible utilizing the currently available methodologies. These techniques utilize the total optimum of the wavelet coefficients with increased brightness while keeping the salient qualities in each image.
4- Fourth step:
By applying the proper threshold values to acquire the best result, the merged images are transformed to a binary format for easy calculation and greater detection effectiveness. According to the suggestion algorithm, the image is read as a 2D matrix consisting of 1 and 0, where 1 represents white color and 0 represents black color. By comparing each pixel with the corresponding pixel in the binary image, the infection can be detected with low error.
5- Fifth step:
After performing the inverse wavelet transform the reconstructed image is obtained. The performance of a reconstructed image is assessed using the statistics Peak Signal to Noise Ratio (PSNR) and Entropy Factor, which vary for the first and second stages of wavelet decomposition. The PSNR is described as (Sapkal and Kulkarni 2012):
PSNR = 20* log (\(\frac{256}{MSE}\)) (8)
Where MSE is the root mean square error which calculated using the formula below:
MSE=[\({\sum }_{i}({r}_{i}-d{)}^{2}\) \({]}^{\frac{1}{2}}\) (9)
Where r, d are the origin and the fused images, respectively. The proposed algorithm's flow chart is shown in Figure (3). The input image's structure can be described using the entropy (E), a numerical value that represents a statistical measure of randomness (Powell et al. 1988):
E= - ∑ (f(I ,j) log2 f(i ,j)) (10)
The histogram of an image is represented as f(I,j). Entropy typically employs 256 bins for 8-bit data and 2 bins for logically arranged arrays.
Figure 4(a, b) show the proposed algorithm on an MRI and a CT images, respectively. The maximal fusion of the generated image is shown in Fig. 4(c).
Table (1) presents the results of image integration using two plane waves, and the resulting image properties are measured by PSNR and entropy. The COVID-19 areas are detected.
Table. 1. performance appraisal of the fused image
Figure (5) depicts the PSNR ratio of the data obtained from various wavelets, including bior2.2, coif2, db2, dmey, rbio2.2, sym4, and haar, we got the highest PSNR value when applying haar waves and its value was 11.195, it was the lowest. The PSNR value when applying the rbio2.2 waves was 11.0579.
Figure (6) displays the entropy values that found with the corresponding values from the various wavelets being bior2.2, coif2, db2, dmey, rbio2.2, sym4, and haar. Entropy is achieved above the first level of decomposition, and it is clearly observed that the dmey waveforms reached a peak of 8.5245.
A technique for merging multifocal images for the identification of COVID-19 to produce a significant image with multispectral data is based on wavelet transduction from computer tomography (CT) and magnetic resonance imaging (MRI) images. It automatically recognizes lung injuries and also identifies their exact position and intensity. The results of the array of images using various wavelengths were compared to the original MRI and CT images in order to determine lung injury based on PSNR and Entropy. It was found that although dmey waves performed best with entropy, haar waves performed best with PSNR. It was discovered that haar waves performed best with PSNR while dmey waves performed best with entropy.
Ethical Approval
not applicable
Competing interests
not applicable
Author contributions
Author 1: Flah A. Bida
-Collected the data
-Contributed data or analysis tools
-Wrote the paper
- Performed the computer simulations
- Performed the statistical analysis
- Performed the text mining analysis
Author 2:Hayder A. Naser
-Conceived and designed the analysis
-Collected the data
-Contributed data or analysis tools
- Performed the text mining analysis
Funding
Funding information is not applicable
Availability of data and materials
not applicable
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No competing interests reported.