Variational Mode Functions Research Articles

Elimination of heart sound from respiratory sound using adaptive variational mode decomposition for pulmonary diseases diagnosis

Lung sound (LS) signals are a vital source of information for the identification of pulmonary disorders. Heart sound (HS) is the most common contaminant of lung sounds during auscultation from the chest walls. This directly affects the efficiency of lung sound processing in diagnosing lung diseases. In this work, Adaptive Variational Mode Decomposition (AVMD) technique is proposed to remove heart sound contaminants from lung sounds. The proposed AVMD method initially breakdown the noisy lung sound signal into a collective of bandlimited modes called variational mode functions (VMF). Then, based on the frequency spectrum, the HS is filtered out from the LS. The real time lung sound data is collected from 95 participants and the performance of VMD technique is evaluated using the statistical metrics measures. Thus, the proposed topology exhibits Higher SNR (29.6587dB, lowest Root Mean Square (RMSE) of 0.0102, lowest normalized Mean Absolute Error (nMAE) of 0.0336, and highest percentage in correlation coefficient Factor (CCF) of 99.79% respectively. These experimental results are found to be superior and outperform all other recently proposed techniques.

A Study on Agricultural Commodity Price Prediction Model Based on Secondary Decomposition and Long Short-Term Memory Network

In order to address the significant prediction errors resulting from the substantial fluctuations in agricultural product prices and the non-linear features, this paper proposes a hybrid forecasting model based on variational mode decomposition (VMD), ensemble empirical mode decomposition (EEMD), and long short-term memory networks (LSTM). This combined model is referred to as the VMD–EEMD–LSTM model. Initially, the original time series of agricultural product prices undergoes decomposition using VMD to obtain a series of variational mode functions (VMFs) and a residual component with higher complexity. Subsequently, the residual component undergoes a secondary decomposition using EEMD. All components are then fed into an LSTM model for training to obtain predictions for each component. Finally, the predictions for each component are linearly combined to generate the ultimate price forecast. To validate the effectiveness of the VMD–EEMD–LSTM model, empirical analyses were conducted for one-step and multi-step forecasts using weekly price data for pork, Chinese chives, shiitake mushrooms, and cauliflower from China’s wholesale agricultural markets. The results indicate that the composite model developed in this study provides enhanced forecasting accuracy.

HEART SOUND NOISE SEPARATION FROM LUNG SOUND BASED ON ENHANCED VARIATIONAL MODE DECOMPOSITION FOR DIAGNOSING PULMONARY DISEASES

Lung sound (LS) signals are vital for diagnosing pulmonary disorders. However, heart sound (HS) interferes with the analysis of LS, leading to the misdiagnosis of lung disorders. To address this issue, we propose an Enhanced Variational Mode Decomposition (E-VMD) technique to remove HS interference from LSs effectively. The E-VMD method automatically determines the mode number for signal decomposition based on the characteristics of variational mode functions (VMFs) such as normalized permutation entropy, kurtosis index, extreme frequency domain, and energy loss coefficient. The performance of the proposed denoising technique was evaluated using six performance metrics: Signal-to-noise ratio (SNR), root mean square error (RMSE), normalized mean absolute error (nMAE), correlation coefficient factor (CCF), CPU[Formula: see text], and CPU[Formula: see text]. In comparison to other denoising methods such as empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), complementary ensemble empirical mode decomposition (CEEMD), singular spectrum analysis (SSA), and variational mode decomposition (VMD), the new E-VMD method demonstrates superior denoising outcome. The proposed method was evaluated using LS recorded from the outpatient department of Thoracic Medicine at Thanjavur Medical College and Hospital, Thanjavur. The obtained performance measures are as follows: RMSE: 0.02103 ± 0.00054, SNR: 28.52464 ± 0.00253, nMAE: 0.00009 ± 0.00056, CCF: 0.9962, CPU[Formula: see text]: 34.586, and CPU[Formula: see text]: 0.452 s. These results affirm the adaptability and robustness of the proposed method, even in the existence of HS noise. This method improves denoising accuracy and computational efficacy, making it a useful tool for improving the analysis of LS signals and assisting in medical diagnostics. This technique utilizes an electronic stethoscope, a common clinical device used by healthcare professionals for detecting lung disease.

Power-line interference and baseline wander elimination in ECG using VMD and EWT

Electrocardiogram (ECG) is a critical biomedical signal and plays an imperative role in diagnosing cardiovascular disorders. During ECG data acquisition in clinical environment, noise is frequently present. Various noises such as powerline interference (PLI) and baseline wandering (BLW) distort the ECG signal which may lead to incorrect interpretation. Consequently, substantial emphasis has been dedicated to ECG denoising for reliable diagnosis and analysis. In this study, a novel hybrid ECG denoising method based on variational mode decomposition (VMD) and the empirical wavelet transform (EWT) is presented. For effective denoising using the VMD and EWT approach, the noisy ECG signal is decomposed within narrow-band variational mode functions (VMFs). The aim is to remove noise from these narrow-band VMFs. In current approach, the centre frequency of each VMF was computed and utilized to design an adaptive wavelet filter bank using EWT. This leads to effective removal of noise components from the signal. The proposed approach was applied to ECG signals obtained from the MIT-BIH Arrhythmia database. To evaluate the denoising performance, noise sources from the MIT-BIH Noise Stress Test Database (NSTDB) are used for simulation. The assessment of denoising performance in based on two key metrics: the percentage-root-mean-square difference (PRD) and the signal-to-noise ratio (SNR). The findings of the simulation experiment demonstrate that the suggested method has lower percentage root mean square difference and higher signal-to-noise ratio as compared to existing state of the art denoising methods. An average output SNR of 24.03 was achieved, along with a 5% reduction in PRD.

Mild cognitive impairment detection with optimally selected EEG channels based on variational mode decomposition and supervised machine learning

Detecting mild cognitive impairment (MCI), which is typically the earliest stage of dementia, is essential for managing dementia. Recently, researchers have explored the use of electroencephalography (EEG) to detect MCI. EEG involves recording brain activity by placing a number of electrodes (channels) directly on the scalp. Here we present effective variational mode decomposition (VMD)-based methods for detection of MCI with optimally selected EEG channels. To achieve this, we first decompose the EEG signals from each channel into sub-signals called variational mode functions (VMFs) with different frequency bands. From each VMF, an entropy measure is used to extract a feature. Several supervised machine learning techniques are investigated to classify the resulting features and obtain full-channel classification accuracy. We assess the classification performance of the proposed methods on 19-channel EEGs recorded from 32 healthy subjects and 29 MCI patients in the resting state. In a second step, we explore the feasibility of reducing the number of EEG channels while maintaining classification accuracy by using several EEG channel selection methods. Specifically, we study the effectiveness of non-dominated sorting genetic algorithm (NSGA)-based methods (multi-objective optimization methods), in addition to greedy algorithms such as back-elimination and forward-addition. Results show that selecting a few suitable channels can lead to similar or even superior accuracy compared to a classifier that utilizes all EEG channels. The results also show that the multi-objective NSGA optimization methods have a greater ability than the greedy methods to select few compatible channels. For example, 99.51% is the maximum accuracy achieved using all 19 EEG channels when processed with a combination of VMD, log energy entropy, and a K-nearest neighbor (KNN) classifier. The same accuracy is achieved with only 9 channels selected by NSGA, compared to 13 channels for greedy algorithms. With an ensemble KNN classifier, the highest accuracy, 99.81%, is achieved using 11 channels selected by an NSGA-based method. The results are encouraging, demonstrating that this brain disorder can be accurately diagnosed using a minimal number of electrodes and paving the way for its adoption in clinical practice.

Variational mode decomposition for surface and intramuscular EMG signal denoising

Electromyographic signals contaminated with noise during the acquisition process affect the results of follow-up applications such as disease diagnosis, motion recognition, gesture recognition, and human–computer interaction. This paper proposes a denoising technique based on the variational mode decomposition (VMD) for both surface electromyography signals (sEMG) and intramuscular electromyography signals (iEMG). sEMG and iEMG obtained from 5 healthy subjects were first decomposed using VMD into respective variational mode functions (VMFs), then thresholds were set to remove the noise, and finally, the denoised signal was reconstructed. The denoising efficacy of interval thresholding (IT) and iterative interval thresholding (IIT) techniques in combination with SOFT, HARD, and smoothly clipped absolute deviation (SCAD) thresholding operators was quantitatively evaluated by using Signal to Noise Ratio (SNR) and further statistically validated by Friedman test. The results demonstrated that IIT provides better SNR values than IT at all noise levels (P-value < 0.05) for sEMG signals. For iEMG, IIT outperformed IT at 0db and 5db noise levels, but at a noise level of 10db and 15db, IT outperformed IIT. However, the results for the 10db noise level were statistically insignificant. The SOFT thresholding operator outperforms HARD and SCAD at all noise levels for sEMG, as well as iEMG (P-value < 0.05). The study demonstrates that the combination of the IIT thresholding technique with the VMD-based SOFT thresholding operator yields the best denoising results while retaining the original signal characteristics. The proposed method can be used in the fields of disease diagnosis, pattern recognition, and movement classification.

Lower limb motion recognition based on surface electromyography

Because the noise in lower limb surface electromyography (sEMG) is so high, extracting characteristics and recognizing lower limb motion is difficult. This research offers an improved threshold algorithm based on parameter α for sEMG signal denoising, convolution neural network (CNN) feature extraction, and kernel extreme learning machine (KELM) classification of lower limb motion recognition to address these issues. First, the sEMG signal decomposes into multiple variational mode functions (VMF) by variational mode decomposition, and the denoised sEMG signal is reconstructed after the VMF is processed by the enhanced threshold algorithm. The denoised sEMG signal is then sent into the CNN network as a matrix to achieve independent feature extraction of the sEMG signal. Finally, KELM is used to classify the retrieved feature signal. The experimental results reveal that this approach has a high signal-to-noise ratio, the root mean square is small, and a good denoising impact. The accuracy of lower limb classification is 95.90%, Based on traditional features and CNN, it is 18.29% and 11.86% higher than KELM, respectively. It can be seen that this research method can improve the accuracy of lower limb motion recognition.

Analysis of Regenerative Raw Signals Using Variational Mode Decomposition

Faults like regenerative tool chatter have been evaluated by several researchers in order to suppress its adverse effect. However, many facets of this domain are yet to be addressed. In the present work, a new methodology has been proposed to process the recorded regenerative chatter signals in order to extract the chatter features. In the proposed approach, experiments have been performed and signals pertaining to regenerative tool chatter have been recorded using microphone. Thereafter, the recorded signals have been evaluated and preprocessed using variational mode decomposition (VMD) in order to extract chatter features. The decomposed signals that result in variational mode functions have been further evaluated by calculating a response termed as chatter index. This response has been used to predict the chatter severity during machining at different combinations of input parameters, on verifying the obtained results it has been found that the proposed methodology is significant in identifying the chatter severity.

Connectedness between Gold and Cryptocurrencies in COVID‐19 Pandemic: A Frequency‐Dependent Asymmetric and Causality Analysis

We employ a frequency‐dependent asymmetric and causality analysis to investigate the connectedness between gold and cryptocurrencies during the COVID‐19 pandemic. Hence, the variational mode decomposition‐based quantile regression is utilised. Findings from the study divulge that the variational mode functions at the lower quantiles are mostly significant and negative indicating that gold acts as a safe haven, a diversifier at most market conditions with insignificant coefficients, and a hedge at normal market conditions for most cryptocurrencies at various investment horizons. Particularly, hedging benefits mostly occur in the short‐ and medium‐term for Bitcoin and Ripple, as well as Bitcoin and Dogecoin in the long‐term with gold. This implies that there is high persistence in the hedging properties of gold with Bitcoin, followed by Ripple. We notice more significant relationship between gold and some cryptocurrencies in the long‐term of the COVID‐19 pandemic relative to the medium‐term emphasising the delayed responses of prices to information. Investors are recommended to be observant and mindful of investing in these markets due to the different dynamics.

Two-Stage Hybrid Machine Learning Model for High-Frequency Intraday Bitcoin Price Prediction Based on Technical Indicators, Variational Mode Decomposition, and Support Vector Regression

Due to the inherent chaotic and fractal dynamics in the price series of Bitcoin, this paper proposes a two-stage Bitcoin price prediction model by combining the advantage of variational mode decomposition (VMD) and technical analysis. VMD eliminates the noise signals and stochastic volatility in the price data by decomposing the data into variational mode functions, while technical analysis uses statistical trends obtained from past trading activity and price changes to construct technical indicators. The support vector regression (SVR) accepts input from a hybrid of technical indicators (TI) and reconstructed variational mode functions (rVMF). The model is trained, validated, and tested in a period characterized by unprecedented economic turmoil due to the COVID-19 pandemic, allowing the evaluation of the model in the presence of the pandemic. The constructed hybrid model outperforms the single SVR model that uses only TI and rVMF as features. The ability to predict a minute intraday Bitcoin price has a huge propensity to reduce investors’ exposure to risk and provides better assurances of annualized returns.

Classification of hand movements using variational mode decomposition and composite permutation entropy index with surface electromyogram signals

Research of human hand movements recognition can be applied to artificial limb control, motion recognition of wearable exoskeleton, human–computer interaction in virtual reality and so on. Surface Electromyogram (sEMG) signal is the preferred source. There are many researches on how to extract information from sEMG signal and apply it to human motion recognition. However, how to extract the feature signal from sEMG signal is a difficult problem in the research of human hand movement recognition based on sEMG signal. In this paper, a method based on Variational Mode Decomposition (VMD) and composite permutation entropy index (CPEI) method is proposed for hand motion classification. Previously, the VMD method had not been used in human hand motion recognition studies. The method proposed in this work applies the VMD method to decompose the original sEMG signal into multiple Variational Mode Functions (VMFs) and calculate the corresponding CPEI of each signal component. Three feature selection methods (Infinite Latent Feature Selection (ILFS), ReliefF, and Laplacian Score) were applied to rank the features and remove the unimportant features. Three classifiers (Naive Bayes, K-NN, and Bagging) were used to recognize the hand actions. Ten volunteers participated in the experiment, and the experimental data were used to verify the proposed method. The average accuracy was 94.28 ± 1.26% for the proposed method with Laplacian Score for feature sorting and selection, and Bagging as classifier. Besides, 600 randomly selected hand movements are predicted (CPU is i5-8250U, ram is 8g, processing software is Spyder, python 3.7), and the corresponding execution time of proposed method is 0.56 s.

VMD-based denoising methods for surface electromyography signals

Objective. Since noise is inevitably introduced during the measurement process of surface electromyographic (sEMG) signals, two novel methods for denoising based on the variational mode decomposition (VMD) method were proposed in this work. Prior to this study, there has been no literature relating to how VMD is applied to sEMG denoising. Approach. The first proposed method uses the VMD method to decompose the signal into multiple variational mode functions (VMFs), each of which has its own center frequency and narrow band, and then the wavelet soft thresholding (WST) method is applied to each VMF. This method is termed the VMD-WST. The second proposed method uses the VMD method to decompose the signal into multiple VMFs, and then the soft interval thresholding (SIT) method is performed on each VMF, which is abbreviated as VMD-SIT. Ten healthy subjects and ten stroke patients participated in the experiment, and the sEMG signals of bicep brachii were measured and analyzed. In this paper, three methods are used for quantitative evaluation of the filtering performance: the signal-to-noise ratio (SNR), root mean square error and R-squared value. The proposed two methods (VMD-WST, VMD-SIT) are compared with the empirical mode decomposition (EMD) method and the wavelet method. Main results. The experimental results showed that the VMD-WST and VMD-SIT methods can effectively filter the noise effect, and the denoising effects were better than the EMD method and the wavelet method. The VMD-SIT method has the best performance. Significance. This study provides a new means of eliminating the noise of sEMG signals based on the VMD method, and it can be applied in the fields of limb movement classification, disease diagnosis, human-machine interaction and so on.

Adaptive spectral smoothening for development of robust keyword spotting system

It is well known that a keyword spotting (KWS) system provides significantly reduced performance in mismatched training and test conditions. In this work, an approach is proposed for reducing the mismatches between the training and test speech due to speaker-related variabilities and environmental noises. In the proposed approach, the variational-mode decomposition is first performed on the short-term magnitude spectra to decompose it into a number of variational mode functions (VMFs) in an adaptive manner. Then, a sufficiently smoothed spectra are reconstructed by selecting only two lower frequency VMFs. When the KWS system is developed by using Mel frequency cepstral coefficients (MFCCs) extracted from the smoothed spectra, a significantly improved performance is observed for pitch and noise mismatched test conditions. To further suppress the mismatches due to the pitch and speaking rate of the speakers, data-augmented training based on explicit prosody modification is performed. The experimental results presented in this study show that data-augmented training further enhances the performance of the developed KWS.

Addressing noise and pitch sensitivity of speech recognition system through variational mode decomposition based spectral smoothing

In this paper, we propose a novel front-end speech parameterization technique for automatic speech recognition (ASR) that is less sensitive towards ambient noise and pitch variations. First, using variational mode decomposition (VMD), we break up the short-time magnitude spectrum obtained by discrete Fourier transform into several components. In order to suppress the ill-effects of noise and pitch variations, the spectrum is then sufficiently smoothed. The desired spectral smoothing is achieved by discarding the higher-order variational mode functions and reconstructing the spectrum using the first-two modes only. As a result, the smoothed spectrum closely resembles the spectral envelope. Next, the Mel-frequency cepstral coefficients (MFCC) are extracted using the VMD-based smoothed spectra. The proposed front-end acoustic features are observed to be more robust towards ambient noise and pitch variations than the conventional MFCC features as demonstrated by the experimental evaluations presented in this study. For this purpose, we developed an ASR system using speech data from adult speakers collected under relatively clean recording conditions. State-of-the-art acoustic modeling techniques based on deep neural networks (DNN) and long short-term memory recurrent neural networks (LSTM-RNN) were employed. The ASR systems were then evaluated under noisy test conditions for assessing the noise robustness of the proposed features. To assess robustness towards pitch variations, experimental evaluations were performed on another test set consisting of speech data from child speakers. Transcribing children's speech helps in simulating an ASR task where pitch differences between training and test data are significantly large. The signal domain analyses as well as the experimental evaluations presented in this paper support our claims.

Variational mode decomposition: mode determination method for rotating machinery diagnosis

Variational mode decomposition (VMD) is a modern decomposition method used for many engineering monitoring and diagnosis recently, which replaced traditional empirical mode decomposition (EMD) method. However, the performance of VMD method specifically depends on the parameter that need to pre-determine for VMD method especially the mode number. This paper proposed a mode determination method using signal difference average (SDA) to determine the mode number for the VMD method by taking the advantages of similarities concept between sum of variational mode functions (VMFs) and the input signals. Online high-speed gear and bearing fault data were used to validate the performance of the proposed method. The diagnosis result using frequency spectrum has been compared with traditional EMD method and the proposed method has been proved to be able to provide an accurate number of mode for the VMD method effectively for rotating machinery applications.

Variational mode decomposition based ECG denoising using non-local means and wavelet domain filtering.

This paper presents a novel electrocardiogram (ECG) denoising approach based on variational mode decomposition (VMD). This work also incorporates the efficacy of the non-local means (NLM) estimation and the discrete wavelet transform (DWT) filtering technique. Current ECG denoising methods fail to remove noise from the entire frequency range of the ECG signal. To achieve the effective ECG denoising goal, the noisy ECG signal is decomposed into narrow-band variational mode functions (VMFs) using VMD method. The idea is to filter out noise from these narrow-band VMFs. To achieve that, the center frequency information associated with each VMFs is used to exclusively divide them into lower- and higher-frequency signal groups. The higher frequency VMFs were filtered out using DWT-thresholding technique. The lower frequency VMFs are denoised through NLM estimation technique. The non-recursive nature of VMD enables the parallel processing of NLM estimation and DWT filtering. The traditional DWT-based approaches need large decomposition levels to filter low frequency noises and at the same time NLM technique suffers from the rare-patch effect in high-frequency region. On the contrary, in the proposed framework both NLM and DWT approaches complement each other to overcome their individual ill-effects. The signal reconstruction is performed using the denoised high frequency and low frequency VMFs. The simulation performed on the MIT-BIH Arrhythmia database shows that the proposed method outperforms the existing state-of-the-art ECG denoising techniques.

Generalized variational mode decomposition for interlayer slipping detection of viscoelastic sandwich cylindrical structures

The viscoelastic sandwich cylindrical structure (VSCS) is widely applied in aerospace, transportation, etc. Its health is closely related to the security of its own service and the entire set of equipment. Therefore, it is very important to detect its operating state. With a focus on the difficulty of weak feature extraction and the lack of efficient interlayer slipping detection indexes for the VSCS, this paper proposes a generalized variational mode decomposition (GVMD) method to extract the weak feature of the VSCS, and constructs a detection index to identify interlayer slipping fault. To this end, first, a GVMD method is proposed to decompose the original signal into a set of band-limited components (called variational mode functions, VMFs) of interest by taking full advantage of prior information such as spectral locations and bandwidths. Then, the vibration signals from the symmetric positions of the VSCS are decomposed by GVMD to extract the VMFs as expected. Finally, the interlayer slipping detection index, namely the normalized energy of the VMFs, is constructed to identify the interlayer slipping fault. And the interlayer slipping symptoms are explored. The effectiveness of GVMD and the proposed detection index is verified by the simulation and the experiment. The results show that: (1) compared with VMD and complementary ensemble empirical mode decomposition, GVMD can expectedly extract feature components (including weak feature components) owing to its excellent performance. (2) The proposed detection index can effectively identify the interlayer slipping fault of the VSCS, and the frequency components near 2× are sensitive to interlayer slipping fault.

Variational mode decomposition based low rank robust kernel extreme learning machine for solar irradiation forecasting

In this paper a new hybrid method has been implemented by combining Variational Mode Decomposition (VMD) and a new low rank robust kernel based Extreme Learning Machine (RKELM) for solar irradiation forecasting. This hybrid model presents an efficient and effective short term solar irradiation prediction approach using the historical solar irradiation data. The original non-stationary time series data is decomposed into various modes using VMD approach. The proposed VMD-RMWK (VMD based reduced Morlet Wavelet Kernel extreme learning machine) method is used to predict the solar irradiation of an experimental 1 MW solar power plant in Odisha, India. Different time intervals of 15 min, 1 h and 1 day ahead in different weather conditions are considered for forecasting purpose. The VMD technique decomposes the original nonlinear irradiation into a set of Variational Mode Functions (VMFs), and the extracted VMFs are used to train the kernel based robust ELM. Comparison with empirical mode decomposition (EMD) based low rank kernel is also presented in this paper. As a new contribution to the previously performed literature survey this paper presents a more accurate solar irradiation prediction paradigm for distinctive weather conditions, and different time intervals varying from very short duration of 15 min to one day ahead. Also to improve the reliability of the KELM and to make it robust under noisy conditions and the presence of outliers in the data, a weight loss matrix has been derived using a non-parametric kernel density estimation method and incorporated in the new formulation (RKELM). A typical solar power experimental solar power station in India has been taken for detailed study showing clearly the accuracy and robustness of the proposed approach. For cross validation of the proposed model, solar irradiation data from a solar power plant located in the state of Florida has been implemented.

Rotational Motions Excited by Vertical Harmonic Motions

The failure of rotating machinery applications has major time and cost effects on the industry. Condition monitoring helps to ensure safe operation and also avoids losses. The signal processing method is essential for ensuring both the efficiency and accuracy of the monitoring process. Variational mode decomposition (VMD) is a signal processing method which decomposes a non-stationary signal into sets of variational mode functions (VMFs) adaptively and non-recursively. The VMD method offers improved performance for the condition monitoring of rotating machinery applications. However, determining an accurate number of modes for the VMD method is still considered an open research problem. Therefore, a selection method for determining the number of modes for VMD is proposed by taking advantage of the similarities in concept between the original signal and VMF. Simulated signal and online gearbox vibration signals have been used to validate the performance of the proposed method. The statistical parameters of the signals are extracted from the original signals, VMFs and intrinsic mode functions (IMFs) and have been fed into machine learning algorithms to validate the performance of the VMD method. The results show that the features extracted from VMD are both superior and accurate for the monitoring of rotating machinery. Hence the proposed method offers a new approach for the condition monitoring of rotating machinery applications.

Noise Removal in Microarray Images Using Variational Mode Decomposition Technique

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.