De-noising Algorithm Research Articles

Transformer enhanced autoencoder rendering cleaning of noisy optical coherence tomography images.

Optical coherence tomography (OCT) is an emerging imaging tool in healthcare with common applications in ophthalmology for detection of retinal diseases, as well as other medical domains. The noise in OCT images presents a great challenge as it hinders the clinician's ability to diagnosis in extensive detail. In this work, a region-based, deep-learning, denoising framework is proposed for adaptive cleaning of noisy OCT-acquired images. The core of the framework is a hybrid deep-learning model named transformer enhanced autoencoder rendering (TEAR). Attention gates are utilized to ensure focus on denoising the foreground and to remove the background. TEAR is designed to remove the different types of noise artifacts commonly present in OCT images and to enhance the visual quality. Extensive quantitative evaluations are performed to evaluate the performance of TEAR and compare it against both deep-learning and traditional state-of-the-art denoising algorithms. The proposed method improved the peak signal-to-noise ratio to 27.9dB, CNR to 6.3dB, SSIM to 0.9, and equivalent number of looks to 120.8dB for a dental dataset. For a retinal dataset, the performance metrics in the same sequence are: 24.6, 14.2, 0.64, and 1038.7dB, respectively. The results show that the approach verifiably removes speckle noise and achieves superior quality over several well-known denoisers.

Sparse-View Neutron Computed Tomography 3-D Reconstruction via the Fast Gradient Projection Algorithm

Neutron tomography is an efficient nondestructive testing technique. As a complement to X-ray computed tomography, it has been widely used in various fields. Due to the difficulty of obtaining complete neutron projection data in a high-radiation environment and the high noise characteristics of neutron images, it is difficult to reconstruct a high-quality image using the conventional filtered-back projection (FBP) algorithm. Therefore, research on sparse-view reconstruction algorithms in neutron tomography is needed. To improve the quality of neutron three-dimensional reconstructed images, this paper proposes an algorithm that combines the Simultaneous Algebraic Reconstruction Technique (SART) with Fast Gradient Projection (FGP), where the FGP is an algorithm for image denoising and deblurring based on the discrete total variation (TV) minimization model. The algorithm proposed in this paper is compared with other algorithms (FBP, SART, and SART-TV) by simulated experimental data and real neutron experimental data. The experimental results show that the novel algorithm outperforms the other three algorithms in terms of denoising and retaining detailed structural information.

Region-based compressive distributed storage in Mobile CrowdSensing

Compressive Sensing-based distributed data storage for Mobile CrowdSensing (MCS) primarily addresses the problem that data needs to be stored temporarily on mobile devices when the central server cannot work as expected. In the crowdsensing-aware platform, the emerging distributed storage scheme mainly recovers the data fields of the entire area. However, when only local area information is required, it is still necessary to recover the entire area, creating unnecessary waste. Based on this observation, this paper proposes a Region-based Distributed Data Storage with global Denoising (R-DDS-D) algorithm. Region-based distributed data storage strategy is individually coded in regional blocks, allowing users to reconstruct the regional information they need selectively. Simultaneously, global denoising can be achieved through the correlation between small regions, which can further improve the accuracy of reconstructed data. In addition, not all local region information is equally significant, an extended algorithm for sampling allocation is proposed considering the importance of different regions to further improve accuracy. Theoretical analysis demonstrates that R-DDS-D can recover the signal with high probability, and the sampling allocation method can more reasonably allocate sampling resources. Experimentally, the R-DDS-D scheme offers greater flexibility, recruiting cost savings, and smoother reconstruction performance for recovering local regions, and the sampling allocation method further enhances the reconstruction quality in the case of uneven data distribution.

A micro-Doppler spectrogram denoising algorithm for radar human activity recognition

Radar signal recognition based on micro-Doppler spectrogram has been widely used in human action recognition tasks. However, in practical application scenarios, radar signals inevitably have noise, which leads to different degrees of deformation of the spectrogram graph structure and affects the accuracy of subsequent recognition algorithms. In this paper, we present “ACFL”, a novel algorithm for micro-Doppler spectrogram denoising, which aims to reduce the impact of noise on human action recognition. ACFL employs amplitude–frequency two-dimensional clustering and fuzzy logic clustering selection mechanism to remove noise elements from the spectrogram. Moreover, to address the issue of noise leakage or target missing under time-varying noise and action conditions, ACFL adopts spectrogram segmentation based on short-term Rényi entropy. By dividing the spectrogram into intervals with different time–frequency distributions, the dynamic spectrogram denoise over time is achieved. Simulation and measured data experiments demonstrate that the proposed algorithm not only achieves a higher-quality denoised spectrogram but also significantly improves the accuracy of human action recognition under noisy conditions.

Research on Speech Denoising Algorithm for Equipment Trains in Fully Mechanized Mining Working Faces based on CEEMDAN High and Low Frequency Filtering

This paper proposes a high and low frequency filtering denoising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). CEEMDAN to address the issue of noise in speech signals obtained in the environment of fully mechanized mining face equipment trains. This algorithm first decomposes speech signals into multiple Intrinsic Mode Functions (IMFs) in different frequency domains through CEEMDAN, then uses Hilbert-Huang Transform (HHT) to obtain the instantaneous frequency and amplitude of IMFs, calculates the Euclidean distance between IMFs, normalizes it to obtain the average distance between IMFs, and divides the IMFs components into high and low frequency categories based on the average distance. Next, Optimally Modified Log Spectral Amplitude (OMLSA) algorithm and Kalman filtering algorithm are used for the high-frequency and low-frequency IMF components, respectively. Finally, the processed IMF components are reconstructed to obtain a denoised signal. After comparative experiments, the noise reduction algorithm proposed in this paper significantly improves the Signal to Noise Ratio (SNR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (RMSE), and Mean Absolute Distance (MAE) of speech signals obtained in the environment of fully mechanized mining face equipment trains compared to other commonly used noise reduction algorithms.

New non-local mean methods for MRI denoising based on global self-similarity between values

Magnetic resonance imaging (MRI) is a non-invasive medical imaging technique that provides high-resolution 3D images and valuable insights into human tissue conditions. Even at present, the refinement of denoising methods for MRI remains a crucial concern for improving the quality of the images. This study aims to improve the prefiltered rotationally invariant non-local principal component analysis (PRI-NL-PCA) algorithm. We relaxed the original restrictions using particle swarm optimization to determine optimal parameters for the PCA part of the original algorithm. In addition, we adjusted the prefiltered rotationally invariant non-local mean (PRI-NLM) part by traversing the signal intensities of voxels instead of their spatial positions to reduce duplicate calculations and expand the search volume to the whole image when estimating voxels’ signal intensities. The new method demonstrated superior denoising performance compared to the original approach. Moreover, in most cases, the new algorithm ran faster. Furthermore, our proposed method can also be applied to process Gaussian noise in natural images and has the potential to enhance other NLM-based denoising algorithms.

A Temperature Compensation Approach for Micro-Electro-Mechanical Systems Accelerometer Based on Gated Recurrent Unit-Attention and Robust Local Mean Decomposition-Sample Entropy-Time-Frequency Peak Filtering.

MEMS accelerometers are significantly impacted by temperature and noise, leading to a considerable compromise in their accuracy. In response to this challenge, we propose a parallel denoising and temperature compensation fusion algorithm for MEMS accelerometers based on RLMD-SE-TFPF and GRU-attention. Firstly, we utilize robust local mean decomposition (RLMD) to decompose the output signal of the accelerometer into a series of product function (PF) signals and a residual signal. Secondly, we employ sample entropy (SE) to classify the decomposed signals, categorizing them into noise segments, mixed segments, and temperature drift segments. Next, we utilize the time-frequency peak filtering (TFPF) algorithm with varying window lengths to separately denoise the noise and mixed signal segments, enabling subsequent signal reconstruction and training. Considering the strong inertia of the temperature signal, we innovatively introduce the accelerometer's output time series as the model input when training the temperature compensation model. We incorporate gated recurrent unit (GRU) and attention modules, proposing a novel GRU-MLP-attention model (GMAN) architecture. Simulation experiments demonstrate the effectiveness of our proposed fusion algorithm. After processing the accelerometer output signal through the RLMD-SE-TFPF denoising algorithm and the GMAN temperature drift compensation model, the acceleration random walk is reduced by 96.11%, with values of 0.23032 g/h/Hz for the original accelerometer output signal and 0.00895695 g/h/Hz for the processed signal.

Simulation of motion error compensation of CNC with multi-axis linkage

Motion errors can significantly affect the machining accuracy of MACNC. To reduce the motion errors in the operation of CNC, an error compensation algorithm is proposed in the study. Firstly, the motion error measurement and identification method is proposed, and in this way, the MECA based on the third spline fitting is proposed Finally, the effectiveness is verified by simulation experiments. The proposed error measurement method has high measurement accuracy, and the MECA can effectively reduce the machining error value, and its processing time is only 0.012s. The measurement accuracy of the error measurement method proposed in the study reached 98.95%, which was 4.49% and 4.88% higher than the minimum measurement accuracy based on wavelet denoising and genetic algorithm, respectively. When the number of iterations was 5, all three measurement methods achieved the minimum measurement accuracy, and the minimum measurement accuracy of the proposed measurement method was 91.00%, Compared with the minimum measurement accuracy of 93.65% and 94.26% based on wavelet denoising and genetic algorithm, it has decreased by 2.65% and 3.26%, respectively. When disturbed, the accuracy rate of the error compensation algorithm proposed by the research is 93.9%, which is 2%, 2% and 3.5% higher than the minimum values of 91.9%, 91.9% and 90.4% of the three error compensation algorithms based on BP neural network, Particle swarm optimization algorithm and genetic algorithm, respectively. The above results show that the MECA can effectively achieve the error compensation of MACNC, with a fast processing speed, which can effectively workshop Machining efficiency and quality.

Enhancing SDGSAT-1 night light images using a panchromatic guidance denoising algorithm

The Glimmer Imager on board the Sustainable Development Science Satellite 1 (SDGSAT-1) is capable of providing high-resolution nighttime light images. However, the presence of stripe noise and dark current noise in L4A images affects the authenticity of image information, thus limiting its scientific applications. This study proposes a panchromatic guidance denoising algorithm to enhance the quality of nighttime light images based on the spectral consistency properties between the panchromatic and RGB channels. This algorithm utilizes two low-noise panchromatic bands to obtain a denoised light area and subsequently removes a significant amount of noise from non-light areas in the RGB bands based on this light area. Our results indicate that this algorithm can effectively remove noise from SDGSAT-1 nighttime light images, achieving a noise removal rate greater than 99.8% in the selected dark ocean area. It also preserves more reasonable radiometric characteristics and spatial details of high-spatial resolution nighttime light images when compared to other popular denoising algorithms. The perturbation caused by moonlight can be effectively eliminated using this algorithm, which further improves the comparability and application of SDGSAT-1 nighttime light images under different lunar phases.

Revealing the Denoising Principle of Zero-Shot N2N-Based Algorithm from 1D Spectrum to 2D Image.

Denoising is a necessary step in image analysis to extract weak signals, especially those hardly identified by the naked eye. Unlike the data-driven deep-learning denoising algorithms relying on a clean image as the reference, Noise2Noise (N2N) was able to denoise the noise image, providing sufficiently noise images with the same subject but randomly distributed noise. Further, by introducing data augmentation to create a big data set and regularization to prevent model overfitting, zero-shot N2N-based denoising was proposed in which only a single noisy image was needed. Although various N2N-based denoising algorithms have been developed with high performance, their complicated black box operation prevented the lightweight. Therefore, to reveal the working function of the zero-shot N2N-based algorithm, we proposed a lightweight Peak2Peak algorithm (P2P) and qualitatively and quantitatively analyzed its denoising behavior on the 1D spectrum and 2D image. We found that the high-performance denoising originates from the trade-off balance between the loss function and regularization in the denoising module, where regularization is the switch of denoising. Meanwhile, the signal extraction is mainly from the self-supervised characteristic learning in the data augmentation module. Further, the lightweight P2P improved the denoising speed by at least ten times but with little performance loss, compared with that of the current N2N-based algorithms. In general, the visualization of P2P provides a reference for revealing the working function of zero-shot N2N-based algorithms, which would pave the way for the application of these algorithms toward real-time (in situ, in vivo, and operando) research improving both temporal and spatial resolutions. The P2P is open-source at https://github.com/3331822w/Peak2Peakand will be accessible online access at https://ramancloud.xmu.edu.cn/tutorial.

Subjective and objective image quality of low-dose CT images processed using a self-supervised denoising algorithm.

This study aimed to assess the subjective and objective image quality of low-dose computed tomography (CT) images processed using a self-supervised denoising algorithm with deep learning. We trained the self-supervised denoising model using low-dose CT images of 40 patients and applied this model to CT images of another 30 patients. Image quality, in terms of noise and edge sharpness, was rated on a 5-point scale by two radiologists. The coefficient of variation, contrast-to-noise ratio (CNR), and signal-to-noise ratio (SNR) were calculated. The values for the self-supervised denoising model were compared with those for the original low-dose CT images and CT images processed using other conventional denoising algorithms (non-local means, block-matching and 3D filtering, and total variation minimization-based algorithms). The mean (standard deviation) scores of local and overall noise levels for the self-supervised denoising algorithm were 3.90 (0.40) and 3.93 (0.51), respectively, outperforming the original image and other algorithms. Similarly, the mean scores of local and overall edge sharpness for the self-supervised denoising algorithm were 3.90 (0.40) and 3.75 (0.47), respectively, surpassing the scores of the original image and other algorithms. The CNR and SNR for the self-supervised denoising algorithm were higher than those for the original images but slightly lower than those for the other algorithms. Our findings indicate the potential clinical applicability of the self-supervised denoising algorithm for low-dose CT images in clinical settings.

A reliable evaluation approach for multichannel signal denoising algorithms based on a novel arterial pulse acquisition system

BackgroundTactile sensors are utilized to measure multichannel pulse signals in pulse wave analysis (PWA). Owing to noise interferences, researchers have applied various denoising algorithms on multichannel pulse signals. To comprehensively assess these algorithms, numerous evaluation metrics have been proposed. However, these studies did not investigate the noise mechanisms in depth and lacked reference pulse signals, thus making the evaluations insufficiently objective. Materials and methodsAn applicable denoising evaluation approach for multichannel pulse signal algorithms based on an arterial pulse acquisition system is established by superimposing real-world multichannel noise to the reference signals. The system, comprising a SphygmoCor and a uniaxial noise acquisition device, allows us to acquire single-reference pulse signals as well as real-world multichannel noise. ResultsWe assess eight popular denoising algorithms with three evaluation metrics, including amplitude relative error (ARE), mean square error (MSE) and increased percentage signal-noise ratio (SNR%). Our proposed approach provides accurate and objective evaluations of multichannel pulse signal denoising. Notably, classic algorithms for single-channel denoising are not recommended for multichannel denoising. Comparatively, RPCA-based algorithms can denoise pulse signals independently for each channel. ConclusionThis study sets the stage for the establishment of accurate and objective pulse signal denoising evaluations and provides insights for data-driven clinical diagnoses in cardiovascular medicine.

X-Let's Atom Combinations for Modeling and Denoising of OCT Images by Modified Morphological Component Analysis.

An improved analysis of Optical Coherence Tomography (OCT) images of the retina is of essential importance for the correct diagnosis of retinal abnormalities. Unfortunately, OCT images suffer from noise arising from different sources. In particular, speckle noise caused by the scattering of light waves strongly degrades the quality of OCT image acquisitions. In this paper, we employ a Modified Morphological Component Analysis (MMCA) to provide a new method that separates the image into components that contain different features as texture, piecewise smooth parts, and singularities along curves. Each image component is computed as a sparse representation in a suitable dictionary. To create these dictionaries, we use non-data-adaptive multi-scale ( X -let) transforms which have been shown to be well suitable to extract the special OCT image features. In this way, we reach two goals at once. On the one hand, we achieve strongly improved denoising results by applying adaptive local thresholding techniques separately to each image component. The denoising performance outperforms other state-of-the-art denoising algorithms regarding the PSNR as well as no-reference image quality assessments. On the other hand, we obtain a decomposition of the OCT images in well-interpretable image components that can be exploited for further image processing tasks, such as classification.

A fractional integral method inverse distance weight-based for denoising depth images

Denoising algorithms for obtaining the effective data of depth images affected by random noise mainly focus on the processing of gray images. These algorithms are not distinct from traditional image-processing methods, and there is no way to evaluate the effectiveness of denoising after the point cloud transformation of denoised depth images. In this paper, the principle of fractional-order integral denoising is studied in detail and inverse distance weighted interpolation is introduced into a denoising model, which is based on the G–L (Grünwald–Letnikov) fractional-order integral to construct a fractional-order integral with an inverse distance weighted denoising model. The model is used to solve the blurring problem caused by sharp changes at the edge and achieves an excellent denoising effect. By using the optimized fractional-order integral denoising operator to construct a denoising model for depth images, the results of the experiments demonstrate that the fractional-order integral of the best denoising effect achieved by the model is −0.6 ≤ ν ≤ −0.4, and the peak signal-to-noise ratio is improved from +6 to +13 dB. In the same condition, median denoising has a distortion of −30 to −15 dB. The depth image that has been denoised is converted into an image of point clouds, and subjective evaluation indicates that the noise is effectively removed. On the whole, the results demonstrate that the fractional-order integral denoising operator with inverse distance weight shows the high efficiency and the outstanding effect in removing noise from depth images while maintaining the image related to the edge and texture information.

Research on improved black widow algorithm for medical image denoising

Improving the quality of medical images is crucial for accurate clinical diagnosis; however, medical images are often disrupted by various types of noise, posing challenges to the reliability and diagnostic accuracy of the images. This study aims to enhance the Black Widow optimization algorithm and apply it to the task of denoising medical images to improve both the quality of medical images and the accuracy of diagnostic results. By introducing Tent mapping, we refined the Black Widow optimization algorithm to better adapt to the complex features of medical images. The algorithm's denoising capabilities for various types of noise were enhanced through the combination of multiple filters, all without the need for training each time to achieve preset goals. Simulation results, based on processing a dataset containing 1588 images with Gaussian, salt-and-pepper, Poisson, and speckle noise, demonstrated a reduction in Mean Squared Error (MSE) by 0.439, an increase in Peak Signal-to-Noise Ratio (PSNR) by 4.315, an improvement in Structural Similarity Index (SSIM) by 0.132, an enhancement in Edge-to-Noise Ratio (ENL) by 0.402, and an increase in Edge Preservation Index (EPI) by 0.614. Simulation experiments verified that the proposed algorithm has a certain advantage in terms of computational efficiency. The improvement, incorporating Tent mapping and a combination of multiple filters, successfully elevated the performance of the Black Widow algorithm in medical image denoising, providing an effective solution for enhancing medical image quality and diagnostic accuracy.

A Non-Contact Measurement of Animal Body Size Based on Structured Light

To improve the accuracy of non-contact measurements of animal body size and reduce costs, a new monocular camera scanning equipment based on structured light was built with a matched point cloud generation algorithm. Firstly, using the structured light 3D measurement model, the camera intrinsic matrix and extrinsic matrix could be calculated. Secondly, the least square method and the improved segment–facet intersection method were used to implement and optimize the calibration of the light plane. Then, a new algorithm was proposed to extract gray- centers as well as a denoising and matching algorithm, both of which alleviate the astigmatism of light on animal fur and the distortion or fracture of light stripes caused by the irregular shape of an animal’s body. Thirdly, the point cloud was generated via the line–plane intersection method from which animal body sizes could be measured. Finally, an experiment on live animals such as rabbits and animal specimens such as fox and the goat was conducted in order to compare our equipment with a depth camera and a 3D scanner. The result shows that the error of our equipment is approximately 5%, which is much smaller than the error of the other two pieces of equipment. This equipment provides a practicable option for measuring animal body size.

Denoising diffusion MRI: Considerations and implications for analysis

Abstract Development of diffusion MRI (dMRI) denoising approaches has experienced considerable growth over the last years. As noise can inherently reduce accuracy and precision in measurements, its effects have been well characterised both in terms of uncertainty increase in dMRI-derived features and in terms of biases caused by the noise floor, the smallest measurable signal given the noise level. However, gaps in our knowledge still exist in objectively characterising dMRI denoising approaches in terms of both of these effects and assessing their efficacy. In this work, we reconsider what a denoising method should and should not do and we accordingly define criteria to characterise the performance. We propose a comprehensive set of evaluations, including i) benefits in improving signal quality and reducing noise variance, ii) gains in reducing biases and the noise floor and improving, iii) preservation of spatial resolution, iv) agreement of denoised data against a gold standard, v) gains in downstream parameter estimation (precision and accuracy), and vi) efficacy in enabling noise-prone applications, such as ultra-high-resolution imaging. We further provide newly acquired complex datasets (magnitude and phase) with multiple repeats that sample different SNR regimes to highlight performance differences under different scenarios. Without loss of generality, we subsequently apply a number of exemplar patch-based denoising algorithms to these datasets, including Non-Local Means, Marchenko-Pastur PCA (MPPCA) in the magnitude and complex domain, and NORDIC, and compare them with respect to the above criteria and against a gold standard complex average of multiple repeats. We demonstrate that all tested denoising approaches reduce noise-related variance, but not always biases from the elevated noise floor. They all induce a spatial resolution penalty, but its extent can vary depending on the method and the implementation. Some denoising approaches agree with the gold standard more than others and we demonstrate challenges in even defining such a standard. Overall, we show that dMRI denoising performed in the complex domain is advantageous to magnitude domain denoising with respect to all the above criteria.

Removal of Mixed Noise in Hyperspectral Images Based on Subspace Representation and Nonlocal Low-Rank Tensor Decomposition.

Hyperspectral images (HSIs) contain abundant spectral and spatial structural information, but they are inevitably contaminated by a variety of noises during data reception and transmission, leading to image quality degradation and subsequent application hindrance. Hence, removing mixed noise from hyperspectral images is an important step in improving the performance of subsequent image processing. It is a well-established fact that the data information of hyperspectral images can be effectively represented by a global spectral low-rank subspace due to the high redundancy and correlation (RAC) in the spatial and spectral domains. Taking advantage of this property, a new algorithm based on subspace representation and nonlocal low-rank tensor decomposition is proposed to filter the mixed noise of hyperspectral images. The algorithm first obtains the subspace representation of the hyperspectral image by utilizing the spectral low-rank property and obtains the orthogonal basis and representation coefficient image (RCI). Then, the representation coefficient image is grouped and denoised using tensor decomposition and wavelet decomposition, respectively, according to the spatial nonlocal self-similarity. Afterward, the orthogonal basis and denoised representation coefficient image are optimized using the alternating direction method of multipliers (ADMM). Finally, iterative regularization is used to update the image to obtain the final denoised hyperspectral image. Experiments on both simulated and real datasets demonstrate that the algorithm proposed in this paper is superior to related mainstream methods in both quantitative metrics and intuitive vision. Because it is denoising for image subspace, the time complexity is greatly reduced and is lower than related denoising algorithms in terms of computational cost.

GPU Accelerated 3D Tomographic Reconstruction and Visualization From Noisy Electron Microscopy Tilt-Series.

We present a novel framework for 3D tomographic reconstruction and visualization of tomograms from noisy electron microscopy tilt-series. Our technique takes as an input aligned tilt-series from cryogenic electron microscopy and creates denoised 3D tomograms using a proximal jointly-optimized approach that iteratively performs reconstruction and denoising, relieving the users of the need to select appropriate denoising algorithms in the pre-reconstruction or post-reconstruction steps. The whole process is accelerated by exploiting parallelism on modern GPUs, and the results can be visualized immediately after the reconstruction using volume rendering tools incorporated in the framework. We show that our technique can be used with multiple combinations of reconstruction algorithms and regularizers, thanks to the flexibility provided by proximal algorithms. Additionally, the reconstruction framework is open-source and can be easily extended with additional reconstruction and denoising methods. Furthermore, our approach enables visualization of reconstruction error throughout the iterative process within the reconstructed tomogram and on projection planes of the input tilt-series. We evaluate our approach in comparison with state-of-the-art approaches and additionally show how our error visualization can be used for reconstruction evaluation.

A fast and efficient numerical algorithm for image segmentation and denoising

<abstract><p>Image segmentation is the process of partitioning an image into homogenous regions, and represents one of the most fundamental and important procedures in image processing. Image denoising is a process to remove unwanted noise from a digital image, enhancing its visual quality. Various algorithms, like non-local means and deep learning-based approaches, have been developed to remove noise while preserving important image details. Currently, the prevalent application of pattern recognition technology is achieved through the implementation of image segmentation algorithms. In this study, we present a new, highly efficient, and fast computational scheme specifically developed for a phase-field mathematical model of image segmentation. The numerical methodology is based on an operator splitting method (OSM). The split operators are solved by using closed-form analytic solutions and a finite difference method (FDM) with an alternating direction explicit (ADE) method. To show the notable efficiency and rapid computational performance of the proposed computational algorithm, we conduct a series of numerical experiments. Through these computational tests, we confirm a significant contribution to the advancement of methodologies employed in the critical domain of image processing.</p></abstract>