Impulsive Noise Model Research Articles

Genetic Programming to Remove Impulse Noise in Color Images

This paper presents a new filter to remove impulse noise in digital color images. The filter is adaptive in the sense that it uses a detection stage to only correct noisy pixels. Detecting noisy pixels is performed by a binary classification model generated via genetic programming, a paradigm of evolutionary computing based on natural biological selection. The classification model training considers three impulse noise models in color images: salt and pepper, uniform, and correlated. This is the first filter generated by genetic programming exploiting the correlation among the color image channels. The correction stage consists of a vector median filter version that modifies color channel values if some are noisy. An experimental study was performed to compare the proposed filter with others in the state-of-the-art related to color image denoising. Their performance was measured objectively through the image quality metrics PSNR, MAE, SSIM, and FSIM. Experimental findings reveal substantial variability among filters based on noise model and image characteristics. The findings also indicate that, on average, the proposed filter consistently exhibited top-tier performance values for the three impulse noise models, surpassed only by a filter employing a deep learning-based approach. Unlike deep learning filters, which are black boxes with internal workings invisible to the user, the proposed filter has a high interpretability with a performance close to an equilibrium point for all images and noise models used in the experiment.

Performance Evaluation CSMA/CA in MAC Layer and Markov Gaussian Memory Impulse Noise Channels in PHY Layer

There is memory impulse noise in urban outdoor/indoor mobile channels, underwater acoustic channels, powerline communications (PLC) channels, etc. The prior works about network performance evaluation in impulse noise channels considered both the impulse noise in the physical (PHY) layer and CSMA/CA in the media access control (MAC) layer but they used simpler memoryless impulse noise model. In this paper, we propose to use 3-D Markov chain and power iteration method to analyze the throughput of CSMA/CA protocols with finite queue and more general memory impulse noise. The numerical results show that when the impulse noise is strong (impulse noise to Gaussian noise ratio R=150), the normalized throughput would be significantly lower than the case without impulse noise (R=0). Therefore, throughput analysis considering the impulse noise effect is essential.

Digital Filtering Techniques Using Fuzzy-Rules Based Logic Control.

This paper discusses current formulations based on fuzzy-logic control concepts as applied to the removal of impulsive noise from digital images. We also discuss the various principles related to fuzzy-ruled based logic control techniques, aiming at preserving edges and digital image details efficiently. Detailed descriptions of a number of formulations for recently developed fuzzy-rule logic controlled filters are provided, highlighting the merit of each filter. Fuzzy-rule based filtering algorithms may be designed assuming the tailoring of specific functional sub-modules: (a) logical controlled variable selection, (b) the consideration of different methods for the generation of fuzzy rules and membership functions, (c) the integration of the logical rules for detecting and filtering impulse noise from digital images. More specifically, we discuss impulse noise models and window-based filtering using fuzzy inference based on vector directional filters as associated with the filtering of RGB color images and then explain how fuzzy vector fields can be generated using standard operations on fuzzy sets taking into consideration fixed or random valued impulse noise and fuzzy vector partitioning. We also discuss how fuzzy cellular automata may be used for noise removal by adopting a Moore neighbourhood architecture. We also explain the potential merits of adopting a fuzzy rule based deep learning ensemble classifier which is composed of a convolutional neural network (CNN), a recurrent neural networks (RNN), a long short term memory neural network (LSTM) and a gated recurrent unit (GRU) approaches, all within a fuzzy min-max (FMM) ensemble. Fuzzy non-local mean filter approaches are also considered. A comparison of various performance metrics for conventional and fuzzy logic based filters as well as deep learning filters is provided. The algorhitms discussed have the following advantageous properties: high quality of edge preservation, high quality of spatial noise suppression capability especially for complex images, sound properties of noise removal (in cases when both mixed additive and impulse noise are present), and very fast computational implementation.

Optimization of capacity in non-Gaussian noise models with and without fading channels for sustainable communication systems

The highest rate at which information may be reliably sent via a communication link is known as its capacity. In the case of non-Gaussian noise, the capacity of the channel depends on the specific characteristics of the noise, which can cause severe errors and reduce the reliability of communication systems over a fading channel. The Gaussian mixture impulsive noise model (GMINM), which is a more general and flexible non-Gaussian model for impulsive noise, has been compared in this paper with the Middleton Class-A impulsive noise model (MCAINM) in terms of derived channel capacity normalized by channel bandwidth (C/BW) with and without Rayleigh fading (Rf) channels. It also investigated the trade-off between complexity and accuracy in modeling the impulsive noise using two simplified Middleton Class-A impulsive noise models based on derived C/BW. The derived C/BW of these models under various conditions, such as different signal-to-noise ratios and impulsive noise parameters and models, have been performed and evaluated using two different scenarios: the exact method and the semi-analytical method. When the impulsive noise parameters and A are both near 0 in GMINM and MCAINM, respectively, the capacity of the impulsive noise channel is found to be equivalent to that of the Gaussian channel sustainable, as shown by the findings based on Monte-Carlo simulations. We have shown that when the impulsive noise decreases, the capacity increases in all models; however, the capacity of Gaussian noise is higher than the capacity of non-Gaussian noise, which in turn is higher than the capacity of non-Gaussian noise over the Rf channel overall values of SNR in dB. Moreover, multi-channel configuration introduces spatial diversity and multiplexing gains that have been proposed to sustainably optimize the ergodic capacity for the challenge case when the channel state information (CSI) is unknown at the transmitter in non-Gaussian noise over Rf channel. In today's rapidly evolving world, sustainable communication systems play a crucial role in ensuring efficient and responsible utilization of resources. As the demand for wireless communication continues to rise, it becomes imperative to optimize the capacity of communication channels, especially in scenarios involving non-Gaussian noise models and fading channels.

New method for detecting and removing random-valued impulse noise from images

The paper proposes a method for detecting and removing impulse noise in images, which determines the similarity between pixels by distance and the difference in brightness values in the local detector window. An impulse noise model is considered, where distorted pixels take random values and also randomly appear in the image. Pixels identified as pulses are recovered with an adaptive median filter. The impulses are determined in the detector window, whose size is calculated in the Euclidean metric and increases with increasing noise intensity in the image. In the experimental part, we discuss visual differences between familiar methods and the one proposed herein on three images for three different impulse noise intensities. In the approximation of image fragments, it is seen that the proposed method copes with the task in the best way, which is also confirmed by numerical estimates of the quality of image reconstruction from impulse noise based on the peak signal-to-noise ratio and the structural similarity index. The proposed method can be used when solving problems of cleaning images under conditions of distorting impulses and for eliminating distortions caused by adverse weather effects, such as raindrops and snow.

Robust sparse Bayesian learning based on the Bernoulli-Gaussian model of impulsive noise

Traditional sparse reconstruction methods suffer from performance degradation in the presence of impulsive noise. In this paper, we adopt the Bernoulli-Gaussian distribution to model the impulsive noise and introduce the hidden state variables to indicate the state of the noise. Based on the new hierarchical Bayesian model, a robust sparse reconstruction algorithm called Bernoulli-Gaussian robust sparse Bayesian learning (BG-RSBL) is developed through the variational Bayesian inference framework. Different from existing robust reconstruction methods, BG-RSBL does not make sparse assumptions about the impulses and outliers. The employment of the Bernoulli-Gaussian model enables BG-RSBL to adapt to environments with a wider range of impulse densities. Comparative analysis shows that the reconstruction performance can be improved by including the outliers in posterior inference with appropriate weightings. Simulations performed under both Bernoulli-Gaussian and symmetric α-stable distributed impulsive noise demonstrate the robust and outstanding reconstruction performance of the proposed algorithm.

Spectral Efficiency Performance of Multi Cell MIMO Systems in Impulsive Noise Channels

This research report details how impulsive noise affects communication systems. This research evaluates the differences and similarities among impulse models in communication systems. After comparing and contrasting the impulse noise models' similarities and differences, the models' service execution will be compared. Spectral efficiency is the fundamental criterion for comparing models' service execution. Comparing models under different impulse noise levels and inter- cell and intra-cell intercession will also be done. The 5G mm Wave multiple input/output system's service execution will be researched. The study will use IN. First, the Gaussian noise scenario will be deduced for the stated device's performance, followed by the non- Gaussian noise scenario derivation. The latter deriva- tion also involves averaging Gaussian noise in terms of impulsive noise's spread. Monte Carlo simulations are used to show and support derivations.

Analysis of Wireless Communication Over Electromagnetic Impulse Noise Channel

Wireless communication in power grid environment faces peculiar power system environment specific noise. Owing to its impulsive nature, the characterization of such noise is critically important and fundamentally different from the existing analysis. This paper presents a theoretical analysis of the impact of power system electromagnetic impulse noise in smart grid environment on the performance of wireless communication between the grid health monitoring devices (e.g., Phasor Measurement Units) and the local data concentrator. It uses a classical approach to the derivation of a re-parameterized impulse noise model from its characteristic function. A comparison of outage probability between the corona impulse noise (CIN)-ridden and noise-free channel is studied. The study is extended for comparison with co-channel interference (CCI) for establishing a better understanding of the power specific electromagnetic impulse noise. A modified performance metric called signal-to-pulse-noise ratio is defined and its probability distribution is derived and compared with the additive white Gaussian noise, CIN and CCI-ridden channel statistics. The physical layer wireless channel characterization analysis is extended further to study the average system throughput via Markov modeling of the channel.

LFM Signal Parameter Estimation via FTD-FRFT in Impulse Noise

LFM signals are widely applied in radar, communication, sonar and many other fields. LFM signals received by these systems contain a lot of noise and outliers. In order to suppress the interference of strong impulse noise on target signals and realize the accurate estimation of LFM signal parameters, the impulse noise of echo signals need to be filtered. In this paper, to solve the problem of poor performance of LFM signal parameter estimation based on fractional Fourier transform in impulse noise, alpha stable distribution is used to establish the mathematical model of impulse noise. The proposed fastest tracking differentiator with an adaptive tracking factor is used to suppress the strong impulse noise, and fractional Fourier transform is used to estimate the parameter of the LFM signals. The experimental results show that the proposed fastest tracking differentiator with an adaptive tracking factor has a good filtering performance. It can effectively filter the impulse noise in the echo signal and allows the FrFT method to accurate estimate the parameters of the LFM signals in strong impulse noise.

GMM-Based Symbol Error Rate Analysis for Multicarrier Systems With Impulsive Noise Suppression

Theoretical analysis of orthogonal frequency division multiplexing (OFDM) systems, equipped at the receiver by a non-linear impulsive noise suppressor, is very challenging. Indeed, although an exact closed-form expression for the output signal-to-noise ratio (SNR) of such OFDM systems is available for widely used impulsive noise models, theoretical analysis of the associated symbol error rate (SER) is still open. The analytical SER available in the literature, exploit a Gaussian approximation of the non-linear distortion noise, which however holds true only under specific conditions. Conversely, this work develops an accurate analytical closed-form expression of the distortion noise distribution at the nonlinearity output, as well as its approximation by a Gaussian mixture model (GMM). By using GMMs we unify the SER analysis for communication systems equipped by non-linear impulsive noise suppressors, typically also used in vehicular communications. Closed form expressions for the SER are derived both for non-fading and frequency-selective Rayleigh/Rician fading channels affected by impulsive noise, which is also modeled by a GMM, including Bernoulli-Gaussian (BG), Middleton Class-A, and alpha-stable noises. Theoretical SER performance are compared with simulations, showing very good agreement for all the impulsive noise scenarios and the non-linear suppressors.

The DOA Estimation Method for Low-Altitude Targets under the Background of Impulse Noise.

Due to the discontinuity of ocean waves and mountains, there are often multipath propagation effects and obvious pulse characteristics in low-altitude detection. If the conventional direction of arrival (DOA) estimation method is directly used for direction finding, it will lead to a large error. In view of serious misalignment in the DOA estimation of multipath signals under the background of impulse noise, a DOA estimation method based on spatial difference and a modified projection subspace algorithm is proposed in this paper. Firstly, the covariance matrix of the received data vector is used for spatial difference to eliminate the multipath effects of low-altitude targets. Secondly, the modified projection matrix is constructed using the signal source estimated with the least squares criterion and then used for modifying the covariance matrix, thus eliminating the cross-covariance matrices that affect the estimation accuracy. Finally, the modified covariance matrix is used for the DOA estimation of targets. Simulations show that the proposed algorithm achieves a higher accuracy in the DOA estimation of low-altitude targets than conventional algorithms under two common impulse noise models, without requiring prior knowledge of impulse noise.

Block-sparse sign algorithm and its performance analysis

System identification is often encountered in applications such as echo cancellation, active noise control, and channel equalization. If the unknown system is sparse, using sparsity-induced methods can improve the convergence performance. Recently, the l2,0-norm constraint was used to derive a block-sparse LMS (BS-LMS) algorithm to accelerate convergence for identifying multi-clustering sparse systems. In some cases, output of the unknown system is contaminated by impulsive noise, and BS-LMS performs poorly or even diverges when identifying such systems. To address this problem, this paper constructs a loss function by combining the absolute error and the l2,0-norm of adaptive filter weight vector, and then uses the subgradient descent method to develop a block-sparse sign algorithm (BS-SA). Its mean and mean-square performance is also analyzed based on the Gaussian-Bernoulli impulsive noise model under some frequently used assumptions. Finally, simulations are performed to test the robustness of BS-SA against impulsive noise and to evaluate the accuracy of theoretical expressions derived for statistical performance.

A Nonparametric Approach to Signal Detection in Non-Gaussian Noise

This letter proposes a nonparametric detector, termed as Gini Correlation (GC), to solve the classical problem of detecting deterministic signals buried in impulsive noise. With the help of the popular Middleton’s Class-A impulsive noise (MCAN) model, we derive the expectation and variance of GC under alternative hypothesis and null hypothesis, which, along with the central limit theorem, are further employed for determining the detection probability and the detection threshold. The results show that the proposed detector possesses a constant false alarm rate property. Monte Carlo simulations verify not only the correctness of our theoretical findings but also the superiority of GC to other state-of-the-art methods in terms of receiver operating characteristic (ROC) curves and asymptotic relative efficiency (ARE) curves.

A LogTVSCAD Nonconvex Regularization Model for Image Deblurring in the Presence of Impulse Noise

This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log-function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data-fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for high-level impulsive noise. A difference of convex functions algorithm (DCA) is proposed to solve the nonconvex model. For the model subproblem, we consider the alternating direction method of multipliers (ADMM) algorithm to solve it. The global convergence is discussed based on Kurdyka–Lojasiewicz. Experimental results show the advantages of the proposed nonconvex model over existing models.

СРАВНИТЕЛЬНЫЙ АНАЛИЗ ДВУХ СПОСОБОВ ФИЛЬТРАЦИИ ДЛЯ УСТРАНЕНИЯ ШУМА В ИЗОБРАЖЕНИИ РАЗНОЙ СТЕПЕНИ ЗАШУМЛЕННОСТИ

In modern photography and video technology, any image in the process of its creation isdistorted by various types of noise. There are various types of noise, but in practice, impulsive andGaussian noise models are the most common. Attenuation of the effect of noise is achieved by filtering.At the moment, there is no universal filter that suppresses noise data at various intens itiesof distortion. Therefore, an important aspect is to determine the field of application of eachtype of filter when suppressing noise in the image and creating a filter, consisting of a combinationof different filtering methods for optimal image cleaning. The article presents a comparativeanalysis of median filtering and Wiener filtering to eliminate impulse and Gaussian noise inthe image with different degrees of noise. For modeling, we used one image, separately distortedby impulse and separately by Gaussian noise with pixel distortion probabilities from 1% to99% inclusive. Filtration was performed with windows equal to 3x3 and 5x5. As a result, weobtained numerical estimates of the image filtering quality based on the peak signal-to-noiseratio (PSNR). On the basis of the data obtained, the application of the investigated filters, theirmodifications, advantages and disadvantages were analyzed, as well as recommendations fortheir use were given. As a result of a comparative analysis of the studied types of filtering fornoisy images, it was found that the median filter with a 3x3 window copes better with imagecleaning from low-intensity impulse noise and with a 5x5 window - with image cleaning with anaverage noise intensity. Also, the median filter does a better job of filtering out Waussian noiseat its medium and high rms deviations. The Wiener filter with 3x3 and 5x5 windows better fi ltersGaussian noise at small values of its root-mean-square deviation. Also, the Wiener filtercopes better with impulse noise with relatively high noise power.

Power Allocation for Wireless Sensor Networks in the Presence of Non-Gaussian Noise and Hardware Impairments Using Distance-Related Bounds

In this letter, we investigate the problem of power allocation in wireless sensor networks, where transceiver hardware impairments (HWIs) at both the sensors and fusion center (FC) are considered. In addition, the received signal at FC is corrupted with the additive non-Gaussian noise, which is characterized by a Gaussian mixture distribution. For this purpose, the Bhattacharyya distance is analyzed as the objective function for formulating the transmit power allocation. Then, we obtain an approximate closed-form expression for the Bhattacharyya distance between two Gaussian mixture distributions. Moreover, the empirical impulsive noise model, i.e., the Bernoulli-Gaussian and the Poisson-Gaussian models, are exploited for the simulation, and the results are compared with each other.

Impulsive noise modeling and robust receiver design

Interference is an important limitation in many communication systems. It has been shown in many situations that the popular Gaussian approximation is not adequate and interference exhibits an impulsive behavior. This paper surveys the different statistical models proposed for such an interference, that can generally be unified using the class of sub-exponential family of distributions, and its impact on the receiver design. Visualizing the optimal decision boundaries allows one to show the non linear effect induced by impulsive noise models, which explains the significant loss in receiver performance designed under the standard Gaussian approximation. This motivates the need to develop new receivers. We propose a framework to design receivers robust to a variety of interference types, both Gaussian and non-Gaussian. We explore three ways of thinking about such receiver designs: a linear approach; by approximating the noise plus interference distribution; and by mimicking the decision rule distribution directly. Except for the linear approach, the other designs are capable of replicating the non-trivial optimal decision regions to different extents. The new detection algorithms are evaluated via Monte Carlo simulations. We focus on four efficient architectures, including the parameter estimations: Myriad, Normal Inverse Gaussian, p-norm and a direct estimation of the likelihood ratio function. They exhibit good performance, close to the optimal, in a large range of situations demonstrating they may be considered as robust decision rules in the presence of heavy tailed or impulsive interference environments.

Rank Correlation Based Detection of Known Signals in Middleton's Class-A Noise

This letter proposes to apply two rank correlations, namely, Kendall's tau (KT) and Spearman's rho (SR), to the fundamental problem of detecting known signals in impulsive noise. Under the popular Middleton's Class-A impulsive noise model, we derived the expectations and variances of KT and SR, which, along with the central limit theorem, are further employed to determing the detection threshold and the detection probability. Monte Carlo simulations not only verified the correctness of our theoretical findings, but also demonstrated the superiority of KT and SR to other five state-of-the-art methods in terms of detection probability.

On Golden Code Performances in Impulsive Noise MIMO Channels

Wireless technologies are the ones who provide fast communications on long distances. MIMO (Multiple-Input-Multiple-Output) Systems become an important factor in communication standards. At the beginning, this technology involved several antennas for both transmission and reception. Nowadays, in order to improve the performance of wireless transmissions, in addition to multi-channel propagation, error correction codes are used. Golden Code has some advantages, such as: maximum rate and diversity or coding gain. In this paper it is proposed an approach of using this code to mitigate the impulsive noise effects in a MIMO communication system. The Middleton Class-A noise was considered. The simulation was done for different values of the impulsive noise model parameters and showed that the probability density function depends on index impulse and on gaussian factor and the number of noise sources has no influence.

Parameter estimation of impulsive noise for channel coded communication systems

In this paper, an impulsive noise estimation algorithm for generating bit log-likelihood ratios (LLRs) for channel coded systems in impulsive noise environments is proposed. This approach is to design the LLR detector in the maximum-likelihood (ML) sense, which requires the parameters of the impulsive noise. The expectation-maximisation (EM) algorithm is utilised to estimate the parameters of the Bernoulli–Gaussian (B–G) impulsive noise model. The estimated parameters is then used to generate the bit LLRs for the soft-input channel decoder. Simulation results show that over a wide range of impulsive noise power, the proposed algorithm approaches the optimal performance (with ideal estimation) even under Middleton class-A (M-CA) impulsive noise models.