Weighted Nuclear Norm Minimization Research Articles

The WIPI Model Based on Multi-Scale Local Contrast Post-Processing for Infrared Small Target Detection

According to the infrared patch image (IPI) model theory, the infrared image background has a low rank and the target is sparse. The low-rank model can be used to separate the background and identify the target. However, in a noisy environment, the recognition effect will be affected. The higher the noise, the harder it would be to detect a small target. The residual strong fault and background edges could reduce the detection rate and increase false alarms. The traditional IPI model is adaptable to the background with the lower noise. This paper combines weighted nuclear norm minimization (WNNM) optimization with sparse representation based on the local IPI model. The background details are described more prominently by improving the nuclear norm weighting factor. The target is much easier to detect under the specific bright clouds and ground buildings background with high noise. At the same time, post-processing with image local contrast analysis is performed to compare traditional spatial filtering and local infrared patch image model algorithms. Our method has a good suppression effect on complex noise backgrounds and achieves a higher signal to clutter ratio gain (SCRG). It could also improve the target detection rate and reduce false alarms.

Image denoising and deringing for fourier single-pixel imaging based on upgraded weighted nuclear norm minimization

Single-pixel imaging techniques have been extensively studied because of the low requirements for the detector resolution and the low equipment cost. However, a large amount of noise and ringing commonly occur in the reconstructed images via previous single-pixel imaging methods at ultra-low sampling rates, which limits the real applications. In this paper, a novel Fourier single-pixel imaging method is proposed to reconstruct high-quality single-pixel imaging images at ultra-low sampling rates, which involves the stages of Fourier single-pixel imaging, block matching, upgraded weight nuclear norm minimization, and aggregation. To decrease the computational burden while important image details, block matching and aggregation are employed for the blocks divided from the low-quality image reconstructed by Fourier single-pixel imaging. To adapt the proposed upgraded weight nuclear norm minimization to different contaminated images, an adaptive scheme for the iterative regularization parameter is proposed to update the traditional weight nuclear norm minimization. Experimental results indicate that the proposed Fourier single-pixel imaging method based on upgraded weight nuclear norm minimization exhibits the capacity to reliably and effectively reconstruct high-quality images for single-pixel imaging at low sampling rates, even at the sampling rate of 1 %. Experimental results also demonstrate that the proposed method performs better image reconstruction than some existing single-pixel imaging.

Multiplicative noise removal using complementary total generalized variation and nonlocal low rank regularization

The problem of multiplicative image denoising is a typical ill-posed inverse problem which has been extensively studied in the past few decades and is still an open problem. Exploiting appropriate image priors is critical to solve ill-posed inverse image restoration problem. The existing total generalized variation (TGV) based approaches have achieved significant performance in removing the multiplicative noise. However, these TGV regularized approaches only consider the local smoothness prior of the potential clean image, which limits their ability for image restoration. Other than the local smoothness property, the nonlocal self-similarity prior of images can also be exploited to offer helpful remedy for better image reconstruction. In this paper, to simultaneously make use of both the local smoothness prior and nonlocal self-similarity prior, we integrate the TGV regularizer with the nonlocal low rank regularizer to propose a novel variational model for multiplicative image denoising. Specifically, in the objective function, the nonlocal low rank regularization is expressed by the celebrated weighted nuclear norm minimization (WNNM) which has recently been applied to image denoising and presents state-of-art result. Then, we apply the split Bregman algorithm to efficiently solve the resulting model. Numerical experiments demonstrate that the proposed method achieve superior performance over the competing methods, including the state-of-the-art SAR-BM3D method.

Denoising for airborne transient electromagnetic data using noise-whitening-based weighted nuclear norm minimization

Abstract Recovering anomalous information covered under noise in late gates can enhance airborne transient electromagnetic (ATEM) detection. Conventional denoising mainly comprises filtering and gate correlation-based decomposition algorithms; the former fails to extract anomalies contaminated by noise and the latter relies on the correlation between gates, which may yield false late gate anomalies caused by early large-amplitude anomalies in early gates. In ATEM profiles, the correlation between anomalies in adjacent gates makes the anomalies to be measured to have low-rank characteristics relative to the noise-contaminated profiles; the noise is uniformly distributed in the profiles, which have nonlocal self-similarity. Therefore, the low-rank matrix approximation algorithm is applicable to ATEM data denoising. In this study, an algorithm—noise-whitening-based weighted nuclear norm minimization (NW-WNNM)—is designed to remove ATEM profile noise. First, we analyze the influence of patch size in block matching on anomalous and noisy patches and estimate the profile patch size adaptively. Then, we combine the estimation of noise variance in weighted nuclear norm minimization (WNNM) with the noise whitening of similar patch matrices to reduce the noise interference on the nuclear norm and add a whitening factor in the weight vector to make the soft-thresholding function applicable to the low-rank reconstruction of the whitened matrix. By analyzing the reconstructed low-rank matrix and its feature distribution, compared with WNNM, NW-WNNM can detect the feature information more accurately and eliminate the influence of noise on the nuclear norm. Simulation and field profile results indicate that NW-WNNM is superior to comparison denoising methods.

GPR Clutter Removal Based on Weighted Nuclear Norm Minimization for Nonparallel Cases

Ground-penetrating radar (GPR) is an effective geophysical electromagnetic method for underground target detection. However, the target response is usually overwhelmed by strong clutter, thus damaging the detection performance. To account for the nonparallel case of the antennas and the ground surface, a novel GPR clutter-removal method based on weighted nuclear norm minimization (WNNM) is proposed, which decomposes the B-scan image into a low-rank clutter matrix and a sparse target matrix by using a non-convex weighted nuclear norm and assigning different weights to different singular values. The WNNM method’s performance is evaluated using both numerical simulations and experiments with real GPR systems. Comparative analysis with the commonly used state-of-the-art clutter removal methods is also conducted in terms of the peak signal-to-noise ratio (PSNR) and the improvement factor (IF). The visualization and quantitative results demonstrate that the proposed method outperforms the others in the nonparallel case. Moreover, it is about five times faster than the RPCA, which is beneficial for practical applications.

A Novel Adaptive Group Sparse Representation Model Based on Infrared Image Denoising for Remote Sensing Application

Infrared (IR) Image preprocessing is aimed at image denoising and enhancement to help with small target detection. According to the sparse representation theory, the IR original image is low rank, and the coefficient shows a sparse character. The low rank and sparse model could distinguish between the original image and noise. The IR images lack texture and details. In IR images, the small target is hard to recognize. Traditional denoising methods based on nuclear norm minimization (NNM) treat all eigenvalues equally, which blurs the concrete details. They are unable to achieve a good denoising performance. Deep learning methods necessitate a large number of train images, which are difficult to obtain in IR image denoising. It is difficult to perform well under high noise in IR image denoising. Tracking and detection would not be possible without a proper denoising method. This article fuses the weighted nuclear norm minimization (WNNM) with an adaptive similar patch, searching based on the group sparse representation for infrared images. We adaptively selected similar structural blocks based on certain computational criteria, and we used the K-nearest neighbor (KNN) cluster to constitute more similar groups, which is helpful in recovering the complex background with high Gaussian noise. Then, we shrank all eigenvalues with different weights in the WNNM model to solve the optimization problem. Our method could recover more detailed information in the images. The algorithm not only obtains good denoising results in common image denoising but also achieves good performance in infrared image denoising. The target in IR images attains a high signal for the clutter in IR detection systems for remote sensing. Under common data sets and real infrared images, it has a good noise suppression effect with a high peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM), with higher noise and a much more complex background.

Inverse Halftoning Based on Weighted Nuclear Norm Minimization

The inverse halftoning technology refers to restoring a continuous-toned image from a halftoned image with only bi-level pixels. However, recovering the continuous images from their halftoned ones is normally ill-posed, which makes the inverse halftoning algorithm very challenging. In this paper, we propose an optimization model with two alternate projections (TAP) for image inverse halftoning under the weighted nuclear norm minimization (WNNM) framework. The main contributions are twofold. First, the WNNM nonlocal regularization term is established, which offers a powerful mechanism of nonlocal self-similarity to ensure a more reliable estimation. Second, the alternate minimization projections are formulated for solving the image inverse halftoning, which reconstructs the continuous-toned image without destroying the image details and structures. The experimental results showed that the proposed method outperformed the state of the arts in terms of both objective measurements and subjective visual performance. The codes and constructed models are available at: https://github.com/juneryoung2022/IH-WNNM.

An edge map-guided acceleration strategy for multi-scale weighted nuclear norm minimization-based image denoising

By exploring the nonlocal self-similarity of images, weighted nuclear norm minimization (WNNM) based image denoising algorithm has achieved competitive performance. Multi-scale patches-based image denoising using weighted nuclear norm minimization (MS-WNNM) is one of the follow-up researches, which further improves WNNM by considering cross-scale self-similarity in block-matching. However, the better performance is achieved at the price of spending more time in a larger search space. In this paper, we propose an edge map-guided strategy to accelerate MS-WNNM based image denoising. Inspired by the fact that patches belonging to the structure part and patches belonging to the texture part follow different repetitive patterns, we propose a prior that the patches containing and surrounding the edges carry most of the structural and textural information of the image. The proposed prior is explained from an information-theoretic perspective. Based on this prior, an edge map-guided acceleration strategy is designed, where redundant patches are trimmed off and the informative patches are retained. Block-matching in the pruned search space, which still has patch diversity, can significantly reduce time without much loss of quality. As a result, comparable denoising can be achieved in less runtime. The experimental results demonstrate the quality and efficiency of the proposed method.

Rank minimization via adaptive hybrid norm for image restoration

Rank minimization methods have achieved promising performance in various image processing tasks. However, there are still two challenging problems in the existing works. One is that most of the current methods only regularize singular values by using a single l1-norm, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM). Consequently, many small singular values are shrunk to zero, which is unbeneficial for restoring image details. The other is that how to adaptively evaluate the importance of each singular value is still a suspending problem. In this paper, we propose a novel rank minimization method, namely adaptive hybrid norm minimization (AHNM) model, to solve the above problems. Specifically, for each singular value, we employ l2-norm to compensate for l1-norm, and introduce a significance factor to assess its importance adaptively. More importantly, we show that closed-form solutions for all subproblems can be derived simply by using alternating optimization. With the aid of the proposed AHNM model, we further develop a general yet effective image restoration algorithm based on the nonlocal self-similarity (NSS) of images. Numerous experimental results demonstrate that the proposed AHNM model consistently outperforms many state-of-the-art restoration methods, including model-based methods and deep learning-based methods.

Infrared Target-Background Separation Based on Weighted Nuclear Norm Minimization and Robust Principal Component Analysis

The target detection ability of an infrared small target detection (ISTD) system is advantageous in many applications. The highly varied nature of the background image and small target characteristics make the detection process extremely difficult. To address this issue, this study proposes an infrared patch model system using non-convex (IPNCWNNM) weighted nuclear norm minimization (WNNM) and robust principal component analysis (RPCA). As observed in the most advanced methods of infrared patch images (IPI), the edges, sometimes in a crowded background, can be detected as targets due to the extreme shrinking of singular values (SV). Therefore, a non-convex WNNM and RPCA have been utilized in this paper, where varying weights are assigned to the SV rather than the same weights for all SV in the existing nuclear norm minimization (NNM) of IPI-based methods. The alternate direction method of multiplier (ADMM) is also employed in the mathematical evaluation of the proposed work. The observed evaluations demonstrated that in terms of background suppression and target detection proficiency, the suggested technique performed better than the cited baseline methods.

Vomiting Management and Effect Prediction after Early Chemotherapy of Lung Cancer with Diffusion-Weighted Imaging under Artificial Intelligence Algorithm and Comfort Care Intervention.

This aim of this research was to explore the evaluation and prediction value of diffusion-weighted imaging (DWI) under artificial intelligence algorithm in the vomiting management and chemotherapy of early lung cancer under comfort care. 118 patients with lung cancer were included as the research objects. They were randomly divided into the control group (routine care) and the experiment group (comfort care) with 59 cases in each. The DWI under the weighted nuclear norm minimization (WNNM) noise reduction algorithm was used for examinations. The noise reduction effect of the algorithm under different Gaussian noises, as well as the sensitivity, specificity, and area under the curve (AUC) of the apparent diffusion coefficient (ADC) maps under different b values, was compared and analyzed. The indicators of vomiting, psychological state, quality of life, serum tumor marker levels, and nursing satisfaction were also compared between the two groups of patients after chemotherapy. Compared to the photon mapping (PM) algorithm and the total variation (TV) norm minimization algorithm, the WNNM algorithm had the most ideal noise reduction effect with clearer images, which was conducive to identification. When the b value was 800 s/mm2, the ADC chart had the best sensitivity, specificity, and AUC values of 0.95, 0.89, and 0.87, respectively. After chemotherapy, 45.76% of patients in the experiment group had vomiting in degree 0 and 40.68% had that in degree I, which suggested that the incidence of vomiting was significantly lower than that in the control group (P < 0.05). All of the psychological state, quality of life, serum tumor marker levels, and nursing satisfaction of patients in the experiment group were significantly better than those in the control group (P < 0.05). It showed that comfort care could alleviate the vomiting response effectively of patients with lung cancer after chemotherapy and had significant effects in improving the quality of life, the psychological state, and curative effect of patients. WNNM algorithm had the better noise reduction effect in DWI image processing. This work provided a certain reference for the nursing intervention plan after chemotherapy of early lung cancer.

Evaluation of Weighted Nuclear Norm Minimization Algorithm for Ultrasound Image Denoising

Anatomical structures manifested in ultrasound (US) images are crucial in efficient disease diagnosis. This modality has been used to analyze different tissue properties, such as blood flow, in-depth tissue motion, and elasticity. Analysis of these US images is posing a critical challenge, as these images are corrupted with noise primarily induced during acquisition. The biological structures intended to be investigated need to be detected, enhanced, and preserved during image processing-based diagnosis. US-based common carotid artery (CCA) images were considered in this study, and five denoising techniques were explored for noise removal after converting the images to grayscale to identify efficient preprocessing for effective diagnosis. Furthermore, filtered images were subjected to different entropy-inspired segmentation for qualitative validation and to segment the CCA. The objective of this paper is a deliberate attempt to investigate the possible use of edge- and structure-preserving filtering techniques to segment tissues of interest. The weighted nuclear norm minimization (WNNM) approach appears to be effective in removing noise and simultaneously preserving the sensitive structures. Quantitative validation with peak signal to noise ratio (PSNR), structural symmetry index measure (SSIM), and feature similarity index measure (FSIM) found to be 27.84 ± 1.04 dB; 0.76 ± 0.01 and 0.87 ± 0.01 were observed to be superiorly high with WNNM filtering. The input image and the filtered image histograms are also compared for qualitative validation. The key finding in this study can be attributed to the ability to remove noise from US images corrupted with noise while preserving the anatomical details. Furthermore, it can be hypothesized that the anatomical structures under the influence of noise can be efficiently preprocessed and can be fed as a viable image towards segmentation followed by recognition and morphological inference.

Speech Enhancement for Robust Speech Recognition Using Weighted Low Rank and Sparse Decomposition Models under Low SNR Conditions

Noise estimation is a crucial stage in speech enhancement (SE), and it commonly necessitates the use of prior models for speech, noise, or both. Prior models, on the other hand, can be ineffective in dealing with unseen nonstationary noise, especially at low signal to noise (SNR) levels. This paper proposes to assess the efficacy of an unsupervised SE approach based on weighted low rank and sparse matrix factorization to estimate noise and speech when neither is available beforehand by decomposing the input noisy spectrum into a low-rank noise component and a sparse speech component. Due to the approximation of the actual rank of noise, these techniques are constrained, and they do not directly exploit the low-rank property in optimization. Nuclear norm minimization (NNM) is the most well-known approach, as it can precisely recover the matrix's rank under certain restricted and theoretical guarantee conditions. NNM, on the other hand, is unable to reliably estimate the matrix rank in many situations. Significant advancements in computer vision and machine learning applications have demonstrated that a weighted nuclear norm minimization (WNNM), overcomes NNM shortcomings, and achieves a superior matrix rank approximation than NNM. Consequently, in this study, we present alternate SE algorithms that make use of weighted low rank and sparsity constraints to separate speech and noise spectrograms. Following that, they were trained and evaluated on a standard Automatic Speech Recognition (ASR) engine to lower the Word Error Rate (WER). Extensive investigations on the impact of real-world noise on speech signals show that the proposed model outperforms the existing state of art models in terms of objective measures like SDR, PESQ, SIG, BAK, OVL, and STOI values in varied noise circumstances under low SNR environments.

Quaternion-based weighted nuclear norm minimization for color image restoration

Color image restoration is one of the basic tasks in pattern recognition. Unlike grayscale image, each color image has three channels in the RGB color space. Due to the inner-relationship within the three channels, color image restoration is usually much more difficult than its grayscale counterpart. Indeed, new problems such as color artifacts could emerge when the grayscale image processing methods are extended to color images directly. Note that one of the most effective gray image restoration methods is the weighted nuclear norm minimization (WNNM) approach. However, when applied to color images, the results of WNNM are usually not as promising as that of grayscale images. In order to solve this problem, in this paper, we propose to restore color images with the quaternion-based WNNM method (QWNNM) since the structure of color channels can be well preserved with quaternion representation. The proposed model can be solved efficiently by the alternating direction method of multipliers (ADMM). The theoretical analysis of the optimal solution is also presented. Numerical experiments are carefully conducted with different kinds of degradation to illustrate the superior performance of our proposed QWNNM over the state-of-the-art methods, including a celebrated deep learning approach, in both visual quality and numerical results.

A Blind SAR Image Despeckling Method Based on Improved Weighted Nuclear Norm Minimization

Coherent imaging of synthetic aperture radar (SAR) systems generates multiplicative speckle noise, severely impairs SAR images’ interpretability. Although numerous despeckling methods have been proposed over the past three decades, SAR despeckling remains an unsolved problem due to its uniqueness and complexity. To address these issues, we propose a novel SAR image despeckling method based on the framework of weighted nuclear norm minimization (WNNM). First, a Gaussian function is used to approximate the distribution of good similar patches (GSP). Clustering is then used to select the optimal patches for the GSP matrix. WNNM can then estimate the underlying clean component of the GSP matrix. To increase the speed of the WNNM, a modified version of the singular value decomposition (SVD) is introduced. Additionally, we developed a noise variance estimation method that enables blind despeckling with the proposed method. Extensive experimental results demonstrate that the proposed method yields superior objective indices and subjective visual inspection.

Spatial-temporal low-rank prior for low-light volumetric fluorescence imaging

In biological fluorescence imaging, obtaining high spatial-temporal resolution volumetric images under low light conditions is one of the critical requirements. As a widely-used snapshot volumetric imaging modality, light field microscopy has the problem of impeded imaging performance caused by reconstruction artifacts, especially under low light conditions. Fortunately, low-rank prior-based approaches have recently shown great success in image, video and volume denoising. In this paper, we propose an approach based on the spatial-temporal low-rank prior combining weighted nuclear norm minimization (WNNM) denoising and phase-space 3D deconvolution to enhance the performance of light field microscopy (LFM) under low light conditions. We evaluated the method quantitatively through various numerical simulations. Experiments on fluorescence beads and Drosophila larvae were also conducted to show the effectiveness of our approach in biological applications.

An Improved Image Filtering Algorithm for Mixed Noise

In recent years, image filtering has been a hot research direction in the field of image processing. Experts and scholars have proposed many methods for noise removal in images, and these methods have achieved quite good denoising results. However, most methods are performed on single noise, such as Gaussian noise, salt and pepper noise, multiplicative noise, and so on. For mixed noise removal, such as salt and pepper noise + Gaussian noise, although some methods are currently available, the denoising effect is not ideal, and there are still many places worthy of improvement and promotion. To solve this problem, this paper proposes a filtering algorithm for mixed noise with salt and pepper + Gaussian noise that combines an improved median filtering algorithm, an improved wavelet threshold denoising algorithm and an improved Non-local Means (NLM) algorithm. The algorithm makes full use of the advantages of the median filter in removing salt and pepper noise and demonstrates the good performance of the wavelet threshold denoising algorithm and NLM algorithm in filtering Gaussian noise. At first, we made improvements to the three algorithms individually, and then combined them according to a certain process to obtain a new method for removing mixed noise. Specifically, we adjusted the size of window of the median filtering algorithm and improved the method of detecting noise points. We improved the threshold function of the wavelet threshold algorithm, analyzed its relevant mathematical characteristics, and finally gave an adaptive threshold. For the NLM algorithm, we improved its Euclidean distance function and the corresponding distance weight function. In order to test the denoising effect of this method, salt and pepper + Gaussian noise with different noise levels were added to the test images, and several state-of-the-art denoising algorithms were selected to compare with our algorithm, including K-Singular Value Decomposition (KSVD), Non-locally Centralized Sparse Representation (NCSR), Structured Overcomplete Sparsifying Transform Model with Block Cosparsity (OCTOBOS), Trilateral Weighted Sparse Coding (TWSC), Block Matching and 3D Filtering (BM3D), and Weighted Nuclear Norm Minimization (WNNM). Experimental results show that our proposed algorithm is about 2–7 dB higher than the above algorithms in Peak Signal-Noise Ratio (PSNR), and also has better performance in Root Mean Square Error (RMSE), Structural Similarity (SSIM), and Feature Similarity (FSIM). In general, our algorithm has better denoising performance, better restoration of image details and edge information, and stronger robustness than the above-mentioned algorithms.

Temperature accuracy enhancement of ROTDR by weighted nuclear norm minimization algorithm

Raman Optical Time Domain Reflectometer (ROTDR) is widely used in industrial fields because of its distributed temperature measurement characteristics. Temperature accuracy is an important parameter of the ROTDR system, and there are some ways including wavelet denoising and nonlocal mean to improve the temperature accuracy of the system. However, these methods either increase the cost of the system or suffer from the limitations of the method itself. In this paper, we propose and experimentally demonstrate a weighted nuclear norm minimization (WNNM) algorithm for temperature accuracy enhancement. WNNM combines singular value decomposition and adaptive threshold to improve the signal-to-noise ratio (SNR) while avoiding data loss, better preserving the information from the original data, and being less sensitive to data similarity. In addition, the WNNM algorithm does not increase the hardware cost of the system. The experimental results show that the WNNM algorithm can achieve better temperature accuracy in the case of low sampling rates and high SNR.

Speckle filtering of ultrasonic images using weighted nuclear norm minimization in wavelet domain

Medical images such as ultrasound images suffer from multiplicative speckle noise which reduces the contrast of ultrasound images and adversely affects the diagnosis process. Discrete Wavelet transform (DWT) is widely accepted in the area of image processing due to its time localization, multi-resolution and sparseness properties. DWT decomposes the noisy image into approximation coefficients and detail coefficients. The detail wavelet coefficients of clean image have sparsity property, whereas in the case of noisy image, sparsity of detail coefficients is reduced due to the presence of speckle noise. Thus, in the proposed method, low rank based Weighted Nuclear Norm Minimization (WNNM) is applied on detail coefficients to reveal the sparsity property of DWT. WNNM is applied on the group matrix of non-local similar patches of detail subbands of DWT to approximate the low-rank denoised version of the subbands. Moreover, less amount of edge and structure information is present in the approximation coefficients of DWT. Thus, in the proposed method, Non-local Means (NLM) filter with Square-Chord distance is also used to denoise speckle noise from approximation coefficients of DWT. Exhaustive experiments are conducted on various images such as real US images, simulated kidney image and synthetic image. It is observed that the mean improvement in terms of PSNR and CNR values of the proposed hybrid method are 1.50% and 3.81% respectively over WNNM based Despeckling using Low-Rank Approximation (DLRA) method. Qualitative and quantitative analyses show that the proposed hybrid method performed better than existing speckle reduction methods in terms of both speckle reduction and edge preservation.

Prediction of Drug-Target Protein Interaction Based on the Minimization of Weighted Nuclear Norm and Similarity Graph between Drugs and Target Proteins

Identification of drug-target protein interaction plays an important role in the drug discovery process. Given the fact that prediction experiments are time-consuming, tedious, and very costly, the computational prediction could be a proper solution for decreasing search space for evaluation of the interaction between drug and target. In this paper, a novel approach based on the known drug-target interactions based on similarity graphs is proposed. It was shown that use of this method was a low-ranking issue and WNNM (weighted nuclear norm minimization) method was applied to detect the drug-target interactions. In the proposed method, the interaction between the drug and the target is encoded by graphs. Also known drug-target interaction, drug-drug similarity, target-target and combination of similarities were used as input. The proposed method was performed on four benchmark datasets, including enzymes (Es), ion channels (IC), G protein-coupled receptors (GPCRs), and nuclear receptors (NRs) based on the AUC and AUPR criteria. Finally, the results showed the improved performance of the proposed method.