

ORIGINAL ARTICLE 



Year : 2022  Volume
: 47
 Issue : 3  Page : 279286 

Development of a fast fourier transformbased analytical method for COVID19 diagnosis from chest Xray images using GNU octave
Durjoy Majumder
Department of Physiology, West Bengal State University, Kolkata, West Bengal, India
Date of Submission  01Apr2022 
Date of Decision  13Jun2022 
Date of Acceptance  20Jul2022 
Date of Web Publication  8Nov2022 
Correspondence Address: Dr. Durjoy Majumder Department of Physiology, West Bengal State University, Barasat, North 24 Parganas, Kolkata  700 126, West Bengal India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jmp.jmp_26_22
Abstract   
Purpose: Many artificial intelligencebased computational procedures are developed to diagnose COVID19 infection from chest Xray (CXR) images, as diagnosis by CXR imaging is less time consuming and economically cheap compared to other detection procedures. Due to unavailability of skilled computer professionals and high computer architectural resource, majority of the employed methods are difficult to implement in rural and poor economic settings. Majority of such reports are devoid of codes and ignores related diseases (pneumonia). The absence of codes makes limitation in applying them widely. Hence, validation testing followed by evidencebased medical practice is difficult. The present work was aimed to develop a simple method that requires a less computational expertise and minimal level of computer resource, but with statistical inference. Materials and Methods: A Fast Fourier Transformbased (FFT) method was developed with GNU Octave, a free and opensource platform. This was employed to the images of CXR for further analysis. For statistical inference, two variables, i.e., the highest peak and number of peaks in the FFT distribution plot were considered. Results: The comparison of mean values among different groups (normal, COVID19, viral, and bacterial pneumonia [BP]) showed statistical significance, especially when compared to normal, except between viral and BP groups. Conclusion: Parametric statistical inference from our result showed high level of significance (P < 0.001). This is comparable to the available artificial intelligencebased methods (where accuracy is about 94%). Developed method is easy, availability with codes, and requires a minimal level of computer resource and can be tested with a small sample size in different demography, and hence, be implemented in a poor socioeconomic setting.
Keywords: Chest Xray image, COVID19, Fourier analysis, image analysis, pneumonia
How to cite this article: Majumder D. Development of a fast fourier transformbased analytical method for COVID19 diagnosis from chest Xray images using GNU octave. J Med Phys 2022;47:27986 
How to cite this URL: Majumder D. Development of a fast fourier transformbased analytical method for COVID19 diagnosis from chest Xray images using GNU octave. J Med Phys [serial online] 2022 [cited 2023 Mar 24];47:27986. Available from: https://www.jmp.org.in/text.asp?2022/47/3/279/360591 
Introduction   
Severe acute respiratory syndrome (SARSCoV) was first identified in December 2019 in Wuhan, China, caused by a novel corona virus COVID19.^{[1]} The disease had the animal origin, but transmitted from human to human through direct and indirect contacts, aerosols, and droplets. Since the time, it had spread all over the world. On January 30, 2020, the WHO declared that the outbreak of SARSCoV2 was a Public Health Emergency of International Concern.^{[2]} The COVID19 infection has onsets similar to other pneumonias.^{[3]}
Conventionally, COVID19 is detected either by reverse transcription–polymerase chain reaction (RTPCR) or by computer tomography (CT) scan. At present, RTPCR method has lower sensitivity (83.3%) compared to CT scan (97.2%).^{[4]} Detection through RTPCR takes several hours; but realistically, it takes several days due to samples are generally processed in bulk. Contrarily, CT scan machines are costly and hence may not be available in remote and rural areas. However, a chest Xraybased (CXR) imaging method is less costly, generally available in remote and rural areas. Portable CXR machines are also available that enhances the feasibility in rural and even in hospital ward. Hence, due to continuation of the pandemic, a quick and costeffective detection method of COVID19 is indeed needed to stop further spread of the disease by isolating the infected person. This may prevent community transmission. Moreover, an early detection can help to start the treatment early.^{[5],[6],[7],[8]} However, inferring of COVID19 infection through CXR or CT scan requires an expert medical personnel, and in rural setup, this may be unavailable. Moreover, due to sudden and massive increase of the pandemic situation, workload of medical personnel has increased tremendously. Hence, computationalbased diagnosis will be an aid to the present situation.
In recent time, many attempts have made for the development of COVID19 diagnosis through computational methods from CXR images and most of the methods followed AI (artificial intelligence) and deep learningbased algorithm [Table 1]. Although it is claimed that deep learningbased AI techniques can be used to ensure that the diagnosis is accurate, and so far through AIbased methods, 86% efficiency was achieved in diagnosing COVID19 infection.^{[12],[13],[19]} It is opined that machine learning algorithm requires a large and balanced datasets.^{[18]} COVID19 has many variants and different clinical manifestations in different individuals. A study with lung CT images showed that 60% of patients had bilateral lung infection, and 10.7% of patients had only right lung involvement and 5.7% of patients had only left lung involvement.^{[20],[21]} Imagebased computational diagnostic methods rely on image pixels across the different anatomical localization of lungs. Hence, detection of COVID19 infection for a clinical case from CXR images by matching with the large training dataset may not able to diagnose a particular case precisely. Changes in training dataset also change the accuracy level for COVID19 detection from CXR images.^{[22]} Moreover, AIbased methods are still not included in the evidencebased clinical practices.^{[23]} Such limitations may restrict the use of AIbased method in a small demographic region. In majority of the cases, for COVID19 detection from Xray images by computational methods, codes are not available. Hence, to run those algorithms, more sophisticated computational resource, large dataset, and/or computational expertise are required.^{[19]} These are also not available in rural setup. Hence, a userfriendly algorithm and easily available framework are also needed. Moreover, majority of the AIbased algorithm for COVID19 diagnosis are questionable due to different flaws including validation, code availability, consideration of demography, and related diseases (bacterial and viral pneumonia [VP]).^{[24]} Here, we have developed an algorithm within a free and opensource platform (software) and made simple statistical inference to distinguish between COVID19, viral pneumonia (VP), and bacterial pneumonia (BP) cases.  Table 1: Comparison between different algorithms for detection of COVID19
Click here to view 
The Fourier Transform is an important mathematical operational method used since 1965.^{[25]} Application of this method in digital image processing was introduced with the development of Fast Fourier Transform (FFT) algorithm in 1970.^{[26]} Through this method, an image is decomposed into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent. In the frequency domain of the image, each point represents a particular frequency contained in the spatial domain image. It is used in image processing for compression, restoration, resampling, edge detection and noise filtering, frequency, and time shift.^{[27],[28]} In the field of medicine, FFT has many applications for image processing and analysis, namely, reconstruction of discretized images of (CT) and (magnetic resonance imaging), ultrasound, and EEG signal analysis.^{[29],[30],[31],[32],[33]}
Materials and Methods   
Image datasets
The entire image dataset utilized in this study was collected from GitHub repository (https://github. com/arpanmangal/CovidAID). Randomly selected images of CXR (anterior–posterior) supine position of 200 normal (N), 200 COVID19 infected (C19), 200 VP, and 200 BP were utilized in this study. GitHub has a library of publicly available collection of data that can be used further.^{[34],[35],[36]} A representative samples of downloaded lung CXR images are shown in [Figure 1].  Figure 1: A representative sample of downloaded lung chest Xray images from Github repository: Healthy asymptomatic normal (in a), diagnosed COVID19 infected (in b), diagnosed viral pneumonia (in c), and diagnosed bacterial pneumonia (in d)
Click here to view 
Computational platform
All computer codes are developed in Octave platform. Octave is an opensource computational platform available freely from GNU Octave webpage (link url: https://www. gnu. org/software/octave/index). From the download page, Octave is downloaded with windows installer (link url: octave6.2.0w64installer. exe) and installed from the installer in a Acer Aspire 1736Z Pentium ® Dual Core T4200 ® 2.00 GHz 6 GB RAM machine (with Windows 10 × 64) following the wizard. Octave is installed with default installation settings. Now, it is launched from the Start menu. The Octave version 6.2.0 has all the packages and installed by default settings and checked by “pkg list” command. However, if needed, io, control, signal, and image package are installed by execution of the following commands sequentially from the command window:
==========================================
Installation of Packages in Octave
==========================================
> pkg list
> pkg install forge io
> pkg install forge control
> pkg install forge signal
> pkg install image1.0.0.tar.gz
> pkg list
> pkg load io
> pkg load control
> pkg load signal
> pkg load image1.0.0.tar.gz
==========================================
Installation and loading of packages are ensured with the “pkg list” command (it displays the list of all the installed packages with * marked).
2.3. Fourier Transform
The Fourier transform is also called a generalization of the Fourier series. This term can also be applied to both the frequency domain representation and the mathematical function used. The Fourier transform helps in extending the Fourier series to nonperiodic functions, which allows viewing any function as a sum of simple sinusoids.
The Fourier transform of a function f(x) is given by,
and the inverse Fourier transform is
where F(k) can be obtained using inverse Fourier transform.
[F (u, v)] is the frequency domain representation of an image [f (x, y)] of size (M × N). Thus, 2D discrete Fourier transform is:
Fourier transform concept is that any waveform can be constructed using a sum of sine and cosine waves of different frequencies. The exponential in the above formula expression can be expanded into sines and cosines with the variables u and v determining these frequencies. The inverse of the above discrete Fourier transform may be expressed as,
2.4. Algorithm of Fast Fourier Transform
FFT is performed through following algorithm.
Step 1: Open the original image through Paint and single lung (left or right) is cropped and save it with a different file name [Figure 2].  Figure 2: Left lung cropped images: healthy asymptomatic normal (in a), diagnosed COVID19 infected (in b), diagnosed viral pneumonia (in c), and diagnosed bacterial pneumonia (in d)
Click here to view 
Step 2: Cropped image is read.
Step 3: Cropped image is converted to grayscale image.
Step 4: Now, the FFT shift technique is applied on grayscale image. FFT2 command computes the Discrete Fourier Transform of time series, and thus frequency domain signal is obtained from image. FFTSHIFT command moves the zero frequency component to the center of the spectrum. For vectors, FFTSHIFT (X) swaps the left and right half of X. For image matrices, FFTSHIFT (X) swaps the first and third quadrants, the second and fourth quadrants. Then, FFT shift in log scale is plotted. This makes the highest frequency at the center.
Step 5: From log FFT shift, a distribution plot is displayed to depict the frequency or pixels.
Step 6: Distribution plot is saved.
For FFT shift distribution, following codes are written in Editor Window and saved.
============================================
Octave Code for FFT Shift & Distribution Plot
============================================
close all
clear all
clc
# convert original image to grayscale image 
img_gray = imread('C003R.bmp');
#grayscale_image=rgb2gray(img_gray);
figure(1);imshow(img_gray);
title('original image')
#figure(2); imshow(grayscale_image);
title('Grascale image')
print djpg grayimage.bmp # saving of grayscale image
#convert grayscale image to log FFT shift image
c = imread('grayimage.bmp');
cf = fftshift(fft2(c));
cr = radon(c);
figure(3);imshow(log(cf),[])
title('log FFT plot')
#print djpg logFFTshift.bmp # to save log FFTshift image
# distribution plot (row vs column) from log FFT shift 
c30 = fftshift(fft2(cr(:,180)));
c30l = log(1+abs(c30));
figure(4);plot(c30l)
title('distribution plot')
#print djpg distribution.bmp # saving of distribution image
==========================================
Before execution of the codes, file name of the image file is changed (also extension if needed). With the execution from Run prompt, finally a distribution plot is generated. From the distribution plot, the highest peak value is noted and the number of peaks on both sides of the highest peak value is counted above a threshold value 12 (along the Yaxis) and such data are tabulated for both lungs. Threshold value is selected arbitrarily. Thus, the dataset has four columns and 800 rows, where each column have different variables (number of peaks of left lung, highest peak value of left lung, number of peaks of right lung, and highest peak value of right lung) and each row represents different CXR of normal, COVID19, VP, and BP. For each CXR image, data of the highest peak values from both the lungs are averaged and tabulated in the fifth column.
Statistical analysis
Twosided ttest is performed for significance of analysis between the mean values of different groups in pair (the groups are C19 and N, VP and N, VP and C19, BP and N, BP and C19, and BP and VP). Further, in an understanding of data variability of each samples in different disease (infected) groups (C19, VP, and BP), we have performed principal component analysis (PCA) and linear discriminant analysis (LDA).
Results   
With the selection of image file name, the FFT code is executed from run tab; then, the whole code runs automatically. Image file is read and displayed, followed by saving of the image (with gray conversion, if any color is present) and plot of FFT shift, and distribution plot is displayed [Figure 3] and [Figure 4].  Figure 3: FFT shift of cropped images: Healthy asymptomatic normal (in a), diagnosed COVID19 infected (in b), diagnosed viral pneumonia (in c), and diagnosed bacterial pneumonia (in d). FFT: Fast Fourier Transform
Click here to view 
 Figure 4: FFT distribution plot of each cropped lung image: Healthy asymptomatic normal (in a), diagnosed COVID19 infected (in b), diagnosed viral pneumonia (in c), and diagnosed bacterial pneumonia (in d). The highest peak value is noted and the number of peaks on both sides of the highest peak value is counted above a threshold value 12 (along the Yaxis). FFT: Fast Fourier Transform
Click here to view 
From distribution plot, data (highest peak value and number of peaks above a threshold value, as mentioned in the previous section) are collected. From each of the CXR image, data are tabulated. Statistical measures and inference between different groups (C19 and N, VP and N, VP and C19, BP and N, BP and C19, and BP and VP) are evaluated by the ttest, and results are tabulated in [Table 2], [Table 3], [Table 4]. In all the cases, P < 0.001 is considered statistically significant. Comparing the mean values of the highest peak value (from distribution plot of both left and right lungs) between groups (N vs. C19, N vs. VP, C19 vs. VP, C19 vs. BP, and BP vs. VP), it shows a statistical significant difference. Comparing the mean value for the number of peaks for left lung between groups (N vs. C19, N vs. VP, C19 vs. VP, N vs. BP, and C19 vs. BP), it shows a statistical significant difference. Comparing the mean value for the number of peaks for right lung between groups (N vs. C19, N vs. VP, C19 vs. VP, N vs. BP, and C19 vs. BP), it shows a statistical significant difference. Results indicate that the mean value of the maximum peak value of BP and normal (N) is almost similar. From the mean value of number of peaks, it is also difficult to distinguish between VP and BP groups for both the lungs. These results are not statistically significant (NS).  Table 2: The statistical measures of inference for average value (left and right lung) of maximum peak value (along Yaxis) obtained from distribution plot of chest Xray images between different groups
Click here to view 
 Table 3: The statistical measures of inference from number of peaks in the left lung obtained from distribution plot of chest Xray images between different groups
Click here to view 
 Table 4: The statistical measures of inference from number of peaks in the right lung obtained from distribution plot of chest Xray images betweens different groups
Click here to view 
To understand the data, variability/clustering pattern is analyzed further in different infected groups (600 × 4, 200 samples for each group and two variables of two lungs) by PCA and LDA. In both the analyses, BP group is partially overlapped with VP groups; in LDA, it is more prominent than PCAbased clustering [Figure 5].  Figure 5: Clustering of data in different infected groups by PCA (in a) and LDA (in b). PCA: Principal component analysis, LDA: Linear discriminant analysis
Click here to view 
Our data clearly suggest that FFTbased algorithm can clearly distinguish between normal and COVID19 infection as well as between pneumonia (viral or bacterial) and COVID19 infection (mean values between the groups are statistically significant); but unable to differentiate between viral and BP. The data of distribution plot analysis indicate that in pneumonia cases, spread of infection within lung is more compared to COVID19 infection cases. Therefore, it can be apprehended that COVID19 infection is clustered to some regions of lungs. It is to be noted here that the maximum peak value of the distribution plot is in the following order:
Normal > COVID19 > Viral pneumonia≅ Bacterial pneumonia; in BP, even height of the highest peak value is almost same compared to normal.
Discussion   
For easy feasibility, cheap and fast approach of CXR, several methods for COVID19 detection through computational approach are developed for COVID19 detection in the past 2 years. Most of the methods are based on deep learning and AIbased. With this approach so far, the maximum accuracy level has reached 98.55%; however, those reports have several disadvantages– sample size for accuracy testing either missing or very limited and many methods do not compare related symptomatic problems like pneumonia,^{[3]} and if considered, they have coupled viral and BP in accuracy testing [Table 1]. Considering such similar types of infections, about 86% is the maximum accuracy level reached.^{[19]} Moreover, in majority of the published works on methodologies, codes are either not available or available in nonstandardized public domain. Although in this field many computer scientists are working and many consider it as manuallike representation, the unavailability of codes limits its further use and hence clinical applications.^{[24],[37]} Moreover, it is an undeniable fact, employing of deep learning and AIbased methods requires more sophisticated computational resource and computertrained personnel, both are difficult to get in rural and poor socioeconomic setting. There is also a lack of necessary mandate of using AI in clinical application to seek evidencebased medical practices, especially in the era of 4IR.^{[23]} Although in recent time, vaccination initiative has started, several persons are still getting infected even after receiving vaccine. Hence, to start treatment early and to prevent community transmission further, still there is a demand of cheap and easier diagnostic procedure of COVID19 infection. Here, the main purpose of the work is to develop a computational method that is easy to handle with minimal level of computational resource and expertise. Hence, detail procedures are available in stepwise manner.
Here, the developed algorithm is numerical and statisticsbased, considers only two variables (highest peak value and number of peaks); hence, easy to implement in rural and poor socioeconomic condition. Moreover, in majority of the published methods on COVID19 detection from the chest images, algorithmic codes are not available. Here, to address the issues as in reference,^{[24]} we have elaborated all the steps and codes. For number of peak counts, the threshold value 12 is selected arbitrarily, and this is considered in the assessment for all the samples. Other workers can select other value, but should maintain the same value for the assessment of all other samples.
With a large dataset having 20 hospitals across the globe, deep transfer learningbased method differentiates COVID19 and COVID19induced pneumonia with 94% accuracy.^{[38]} However, in another work, it is reported that changing of dataset ANNbased method showed differences in accuracy in detection (94% and 85%), and it also requires large dataset for training purpose.^{[22]} Hence, if images are collected from a single demography and with the same machine, then comparing the mean values between normal volunteers and individual patients' data will help detect COVID19 infection in individual patient. With this method, COVID19 infection is differentiated from pneumonia (bacterial and viral); however, with this method, differentiation between bacterial and VP cannot be differentiated. It is needless to mention here that so far no AI and deep learningbased machine learning algorithm can differentiate between the two. We have made analysis with the images available in public domain, and the images are captured with different machines and possibly from different demographics; however, statistical inference is highly significant (P < 0.001), the calculated P value in turn shows high level of accuracy and sensitivity compared to existing AIbased methods.
This method utilizes FFTbased analysis of pixels distribution (distribution plot); hence, another important finding of the work is that COVID19 infection may be clustered to some regions of lungs; while in pneumonia cases, infection spreading within lung is more. We could not find any significant difference between the left and right lung data within the same group, this in turn, may indicate that there is no specificity of infection among lungs, especially with COVID19 infection. A work utilizes texture, GLDM, GLCM, FFT, and wavelet for feature extractions, followed by uses machine learning classifier to classify normal, COVID19, and pneumonia with 94% accuracy.^{[37]} This work utilizes FFTbased data of two variables which make an ease to perform an elementary parametricbased statistical analysis; hence, contrary to AIbased methods, it does not require large datasets; however, contribute more substantially to evidencebased diagnosis.^{[39]} Such statistical operations are very elementary and available under statistical menu of the spreadsheet program in Office software, both in Microsoft and LibreOffice (another free and opensource software). The developed code is in Octave, a free opensource platform, and it can be installed to a computer with minimum configuration; runtime of the code is a few seconds, and hence, computational cost is very low. All these advantages make the method simple.
Conclusion   
The developed method is based on simple codes (which are also available here) in Octave platform and requires a minimal computer resource, so this can be employed in poor and low socioeconomic setting. It can be accepted and implemented universally to include in different and even in small demography without waiting for large data for generating training dataset as in AI. A suspected patient's CXR image is collected and made a FFTbased analysis. Numerical values obtained from the distribution plot of FFT analysis (number of peaks) will be compared to the mean ± standard deviation value of normal; then, a followup to be made by isolating the patients and if possible, can be referred for further investigation. Although the mean value of the highest peak showed statistical significance among groups, the differences are very less; hence, monitoring the value in the number of peaks is important and can practically be possible. We hope that this analytical method could be applied immediately to combat the community spread of COVID19 infection and to stop this pandemic situation and ultimately causes eradication of the disease.
Acknowledgment
The author acknowledges the critical comments and suggestions of Dr. Dibyendu Kumar Ray, Senior Consultant of Neurosurgery, AMRI Hospital and President, Society for Systems Biology and Translational Research about this work.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2], [Table 3], [Table 4]
