Microarray technology allows the simultaneous monitoring of thousands of genes in parallel. Based on the gene expression measurements, microarray technology have proven powerful in gene expression profiling for discovering new types of diseases and for predicting the type of a disease. Enhancement, Gridding, Segmentation and Intensity extraction are important steps in microarray image analysis. This paper presents a noise removal method in microarray images based on Variational Mode Decomposition (VMD). VMD is a signal processing method which decomposes any input signal into discrete number of sub-signals (called Variational Mode Functions) with each mode chosen to be its band width in spectral domain. First the noisy image is processed using 2-D VMD to produce 2-D VMFs. Then Discrete Wavelet Transform (DWT) thresholding technique is applied to each VMF for denoising.  The denoised microarray image is reconstructed by the summation of VMFs.  This method is named as 2-D VMD and DWT thresholding method. The proposed method is compared with DWT thresholding and BEMD and DWT thresholding methods. The qualitative and quantitative analysis shows that 2-D VMD and DWT thresholding method produces better noise removal than other two methods

Harikiran, J.

Kumar, G. Sai Chaitanya

Kumar, Reddi Kiran

Naidu, G. Apparao

English

TELKOMNIKA (Telecommunication Computing Electronics and Control)

TELKOMNIKA, Vol.15, No.4, December 2017, pp. 1750~1756 
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013 
DOI: 10.12928/TELKOMNIKA.v15i4.5375   1750 
  
Received June 25, 2017; Revised September 18, 2017; Accepted September 30, 2017 
Noise Removal in Microarray Images Using Variational 
Mode Decomposition Technique 
 
 
G. Sai Chaitanya Kumar*
1
, Reddi Kiran Kumar
2
, G. Apparao Naidu
3
, J. Harikiran
4
 
1
Dept of CSE, JNTU Hyderabad, India 
2
Dept of CS, Krishna University, Machilipatnam, India 
3
Dept of CSE, J.B. Institute of Engineering and Technology, Hyderabad, India 
4
Department of IT, GIT, GITAM University, Visakhapatnam, India 
*Corresponding author, e-mail: saijntuhphd@gmail.com 
 
 
Abstract 
Microarray technology allows the simultaneous monitoring of thousands of genes in parallel. 
Based on the gene expression measurements, microarray technology have proven powerful in gene 
expression profiling for discovering new types of diseases and for predicting the type of a disease. 
Enhancement, Gridding, Segmentation and Intensity extraction are important steps in microarray image 
analysis. This paper presents a noise removal method in microarray images based on Variational Mode 
Decomposition (VMD). VMD is a signal processing method which decomposes any input signal into 
discrete number of sub-signals (called Variational Mode Functions) with each mode chosen to be its band 
width in spectral domain. First the noisy image is processed using 2-D VMD to produce 2-D VMFs. Then 
Discrete Wavelet Transform (DWT) thresholding technique is applied to each VMF for denoising.   
The denoised microarray image is reconstructed by the summation of VMFs.  This method is named as  
2-D VMD and DWT thresholding method. The proposed method is compared with DWT thresholding and 
BEMD and DWT thresholding methods. The qualitative and quantitative analysis shows that 2-D VMD and 
DWT thresholding method produces better noise removal than other two methods. 
 
Keywords: Empirical Mode decomposition, Variational Mode Decomposition, Discrete Wavelet Transform, 
Image Enhancement, Microarray Images 
 
Copyright © 2017 Universitas Ahmad Dahlan. All rights reserved. 
 
 
1. Introduction 
The most powerful tool in molecular genetics for biomedical research is Microarray, 
which allows parallel analysis of the expression level of thousands of genes. The most important 
aspect in microarray experiment is image analysis. The output of image analysis is a matrix 
consisting of a measure of intensity of each spot in the image. This measure denotes gene 
expression ratio (transcription abundance) between the test and control samples for the 
corresponding gene. The positive expression indicates the over-expression, while negative 
expression indicates under-expression between the control and treatment genes. The main 
components in microarray image analysis are localization, segmentation and spot  
quantification [1]. This paper mainly focuses on Gaussian noise removal in microarray images. 
The main applications of microarray technology are Gene discovery, Drug discovery, Disease 
diagnosis, Toxicological research etc [2]. The microarray image analysis is shown in Figure 1. 
The evaluation of microarray images is a difficult task as the fluorescence of the glass 
slide adds noise floor to the microarray image. The processing of the microarray image requires 
noise suppression with minimal reduction of spot edge information that derives the 
segmentation process. Thus the task of microarray image enhancement is of paramount 
importance [3]. This paper presents a Gaussian noise removal in microarray images using 
Variational Mode Decomposition. First the noisy image is decomposed in to VMFs using 2-D 
VMD. Each VMF is denoised using DWT thresholding technique. After denoising, the image is 
reconstructed by combining all 2-D VMFs. After noise removal, gridding, segmentation and 
Expression ratio calculation are the important tasks in microarray image analysis [4]. Any noise 
in the microarray image will affect the subsequent analysis. The paper is organized as follows: 
Section 2 presents Denoising using DWT Thresholding method, Section 3 presents Denoising 
using Bi-dimensional Empirical Mode Decomposition (BEMD) and DWT thresholding method, 
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Noise Removal in Microarray Images using Variational Mode … (G. Sai Chaitanya Kumar) 
1751 
Section presents Denoising using 2-D VMD and DWT thresholding method, Section 5 presents 
FCM Clustering Algorithm, Section 6 presents Experimental results and Section 7 report 
conclusions. 
 
 
 
 
Figure 1. Microarray Image Analysis 
 
 
2. Discrete Wavelet Transform (DWT) Thresholding Method 
The algorithm of microarray image denoising using Discrete Wavelet Transform (DWT) 
is summarized as follows:  
a. Perform multiscale decomposition [5] of the image corrupted by Gaussian noise using 
wavelet transform. 
b. Estimate the noise variance σ
2
. The noise variance is estimated from sub-band HH1 
using the formula 
 
2
2
(
, 1
0.6745
ij
ij
median y
y subbandHH
 
  
  
     (1) 
c. For each level, compute the scale parameter β using [6] 
 
log k
L
J
 
 Lk is the length of the sub-band at k
th
 scale.   (2) 
 
d. For each sub-band (except the low pass residual)  
1. Compute the standard deviation σy.  
2. Apply soft thresholding to the noisy coefficients. The thresholds used by wavelets for filtering 
are universal threshold [7], SURE shrink [8], Bayes shrink [9] and Normal shrink [10]. 
e. Invert the multiscale decomposition to reconstruct the denoised image. 
 
 
3. BI-Dimensional Empirical Mode Decomposition and DWT Thresholding Method 
Empirical mode decomposition [11] is a signal processing method which divides any 
signal into number of oscillatory functions called intrinsic mode functions (IMF). Each IMF 
satisfies two properties given in [12].  The first IMF is high frequency component and last IMF is 
low frequency component. The shifting process [13] used to obtain IMFs on a 2-D signal 
(microarray image) is summarized as follows: 
a. Find all local maxima and local minima points in I(x,y). 
b. Interpolate the local maxima and local minima points using cubic spline interpolation 
method to create envelopes. (Up(x,y) upper envelope and Lw(x,y) lower envelope) 
 
( ( , ) ( , ))
( , )
2
Up x y Lw x y
Mean x y


      (3) 
 Raw 16 bit DNA 
microarray image 
Image 
Enhancement 
Segmentation Output: Spot 
Metrics 
Gridding 
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          (4) 
 
        (5) 
 
              (6) 
 
Repeat the above steps (b) to (f) for the generation of next IMFs. This process is repeated until 
I(x,y) does not have maxima or minima points to create envelopes. Original Image can be 
reconstructed by inverse EMD given by 
 
      (7) 
 
The mechanism of de-noising using BEMD and DWT is summarized as follows: 
a. Apply 2-D EMD for noisy microarray to obtain IMFi (i=1, 2, …k). The kth IMF is called 
residue. 
b. The first few IMFs contains high frequency components and it is suitable for denoising 
and denoised with DWT Thresholding technique presented in section 2. This de-noised 
IMF is represented with DNIMF. 
c. The denoised image is reconstructed by the summation of DNIMF and remaining IMFs 
given by  
 
2
1
k
i
i
RI DNIMF IMF

 
       (8) 
 
Where RI is the reconstructed band. The flow diagram of BEMD and DWT filtering is shown in 
Figure 2. 
 
 
 
 
Figure 2. BEMD and DWT filtering 
 
 
4. Variational Mode Decomposition and DWT Threshonding Method 
The mechanism of de-noising using 2-D VMD and DWT is summarized as follows 
a. Apply 2-D VMD for noisy microarray to obtain VMFi (i=1, 2,…k). The kth VMF is called 
residue. The VMD framework is used to decompose any signal into k mode components 
presented in [15] 
b. The VMFs are denoised with DWT Thresholding technique presented in section 2. This 
de-noised VMF is represented with DNVMF. 
c. The denoised image is reconstructed by the summation of VMFs given by  
 
Noisy 
Image 
B 
E 
M 
D 
 
(HF) 
IMF 
 
(LF) 
IMF 
Wavelet  
De-noising 
De-noised  
Image 
TELKOMNIKA  ISSN: 1693-6930  
 
Noise Removal in Microarray Images using Variational Mode … (G. Sai Chaitanya Kumar) 
1753 
1
k
i
i
RI VMF

          (10) 
 
Where RI is the reconstructed image. The flow diagram of 2-D VMD and DWT filtering is shown 
in Figure 3. 
 
 
 
 
Figure 3. 2-D VMD and DWT filtering 
 
 
5. Fuzzy C-Means Clustering Algorithm 
1. Take K cluster centroid values [17] 
2. Initialize membership matrix uij and m=2.  
3. Assign each pixel to the cluster according to the given formula [19]. 
 
     (11) 
 
The new membership and cluster centroid values as calculated as [18] 
            
 
                                          (12) 
 
4. Continue 2-3 until each pixel is assigned to the maximum membership cluster. 
 
 
6. Experimental Results 
In this section, the proposed filtering method is performed on a sample microarray slide 
drawn from the standard microarray database corresponds to breast category aCGH tumor 
tissue. To check the performance of the filtering methods presented in this paper Gaussian 
noise with different values of σ is added to the image. The noisy image is filtered using the three 
methods presented in this paper. The quantitative results are evaluated using PSNR values are 
shown in Table 1 and qualitative results are shown in Figure 4. Both qualitative and quantitative 
results show that 2-D VMD and DWT filtering method has better denoising effect. After 
denoising the image is segmented using FCM clustering algorithm. 
 
 
Noisy 
Image 
2-D 
V 
M 
D 
 
V 
M 
F 
Wavelet  
De-noising 
De-noised  
Image 
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Table 1. PSNR Values of Filtering Method 
Method σ = 0.015 σ = 0.025 σ = 0.036 
Wavelet (Universal Threshold) 22.02 16.98 14.89 
Wavelet ( SURE shrink) 21.90 16.11 13.76 
Wavelet (Bayes Shrink) 20.08 15.72 12.91 
Wavelet (Normal Shrink) 20.98 15.23 13.12 
BEMD + Wavelet (Universal Threshold) 34.11 29.86 23.86 
BEMD + Wavelet (SURE shrink) 32.89 28.74 22.11 
2-D VMD+ Wavelet (Bayes Shrink) 36.16 30.98 24.43 
2-D VMD+ Wavelet (Normal Shrink) 38.91 32.34 26.98 
 
 
Original Image (4a) Gaussian Noise (4b) 
 
 
 
Filtering Using BEMD+DWT (4c) 
 
Filtering Using 2-D VMD+DWT (4d) 
 
 
Segmentation using FCM on filtered image (4e) 
 
 
 
Segmentation using FCM on noisy image (4f) 
 
Figure 4. Qualitative Analysis of Filtering methods 
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Noise Removal in Microarray Images using Variational Mode … (G. Sai Chaitanya Kumar) 
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Figure 4. Qualitative Analysis of Filtering methods 
 
 
7. Conclusions 
Microarray technology is used for parallel analysis of gene expression ratio of different 
genes in a single experiment. The analysis of microarray image is done with gridding, 
segmentation and information extraction. The expression ratio of each and every gene spot 
denotes the transcription abundance between two genes under experiment. This paper presents 
different methods for microarray image denoising. Out of these methods 2-D VMD and DWT 
perform noise suppression in the image and produces better segmentation accuracy. Spot 
information includes the calculation of Expression Ratio in the region of every gene spot on the 
microarray image. The expression-ratio measures the transcription abundance between the two 
sample genes. 
 
 
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Noise Removal in Microarray Images Using Variational Mode Decomposition Technique

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Noise Removal in Microarray Images Using Variational Mode Decomposition Technique

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