Impulsive Noise Model Research Articles

Robust Matched Filtering in <formula formulatype="inline"><tex Notation="TeX">$\ell_{p}$</tex></formula>-Space

A common approach to time-delay estimation (TDE) and joint delay-Doppler estimation (JDDE) for target localization is matched filtering, which is equivalent to the cross correlation of the received and transmitted signals. The conventional correlation in Hilbert space is statistically optimal in white Gaussian noise. However, its performance significantly degrades in the presence of non-Gaussian noise or clutter. In this paper, two new concepts called $\ell_{p}$ -correlation and $\ell_{p}$ -ambiguity functions, which generalize the conventional matched filtering from Hilbert space to $\ell_{p}$ -space, are proposed. In addition, several important mathematical properties of the $\ell_{p}$ -correlation and $\ell_{p}$ -ambiguity functions are given and proved. Compared with conventional ambiguity function, the time-frequency concentration of the $\ell_{p}$ -ambiguity function is significantly enhanced, i.e., the delay-Doppler resolution is improved and the sidelobes are suppressed. Based on these two newly defined functions, a family of TDE and JDDE algorithms that are robust against impulsive noise or clutter are developed. Furthermore, the Cramer–Rao bounds of TDE and JDDE for non-Gaussian noise with arbitrary probability distribution are derived. Simulation results under several impulsive noise models demonstrate that the performance in terms of robustness, resolution, and estimation accuracy is substantially improved when compared with the conventional matched filtering and fractional lower-order moment based methods.

Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV)

In this article, a novel algorithm for denoising images corrupted by impulsive noise is presented. Impulsive noise generates pixels whose gray level values are not consistent with the neighboring pixels. The proposed denoising algorithm is a two-step procedure. In the first step, image denoising is formulated as a convex optimization problem, whose constraints are defined as limitations on local variations between neighboring pixels. We use Projections onto the Epigraph Set of the TV function (PES-TV) to solve this problem. Unlike other approaches in the literature, the PES-TV method does not require any prior information about the noise variance. It is only capable of utilizing local relations among pixels and does not fully take advantage of correlations between spatially distant areas of an image with similar appearance. In the second step, a Wiener filtering approach is cascaded to the PES-TV-based method to take advantage of global correlations in an image. In this step, the image is first divided into blocks and those with similar content are jointly denoised using a 3D Wiener filter. The denoising performance of the proposed two-step method was compared against three state-of-the-art denoising methods under various impulsive noise models.

Optimum linear regression in additive Cauchy–Gaussian noise

We study the estimation problem of linear regression in the presence of a new impulsive noise model, which is a sum of Cauchy and Gaussian random variables in time domain. The probability density function (PDF) of this mixture noise, referred to as the Voigt profile, is derived from the convolution of the Cauchy and Gaussian PDFs. To determine the linear regression parameters, the maximum likelihood estimator (MLE) is developed first. Since the Voigt profile suffers from a complicated analytical form, an M-estimator with the pseudo-Voigt function is also derived. In our algorithm development, both scenarios of known and unknown density parameters are considered. For the latter case, we estimate the density parameters by utilizing the empirical characteristic function prior to applying the MLE. Simulation results show that the performance of both proposed methods can attain the Cramér–Rao lower bound.

A noise-ranking switching filter for images with general fixed-value impulse noises

Impulse noise is generally classified into random-value and fixed-value types. However, most of the previous literatures recognized salt and pepper (S&P) noise as the fixed-value impulse noise because it is easily detected and recovered. This article studies a general fixed-value impulse noise in which the corrupted pixels are set to not only the minimum–maximum values but also any fixed intensities. A novel noise-ranking switching filter (NRSF) is proposed for suppressing these tough noise types. In order to clearly distinguish the noise-free pixels from noisy pixels having the same gray value, the detection stage of NRSF consists of three modified methodologies, named global–local statistics analysis, sectional boundary discriminative noise detection, and a directional test. Once a corrupted pixel has been identified, the same matrix convolution technique used in the last test is employed again in the second NRSF stage to recover the noise. Additionally, it is suggested that the corrupted pixels are processed via the rank of noise density for improving the suppression capability at very high noise ratio. Although the NRSF is driven for a new impulse noise model, it outperforms several state-of-the-art algorithms in terms of noise suppression and detail preservation even for images with the traditional S&P noise.

Image Denoising by Two-Pass of Total Variation Filter

variation based methods are widely applied for image enhancement and particularly for de-noising. The majority of these is designed for a specific noise model. The alternative total variation based approach proposed here can deal with multiple noise models via two-pass iterative algorithm basing on total variation. The first pass is designed for draft denoising and to detect noise region. The second pass restores the noise region by total variation based inpainting. Experiments on Salt & Pepper, Gaussian, Speckle, Poisson, and Impulse noise models demonstrate the effectiveness of the proposed method.

Performance evaluation of max-dmin precoding in impulsive noise for train-to-wayside communications in subway tunnels

This paper addresses the performance evaluation of the multiple input multiple output (MIMO) precoding technique, referred to as max-dmin precoding, over fading channel with impulsive noise in a railway tunnel. Measurements showed that the received signal at the antenna on the moving train roof near the catenary suffers from electromagnetic noise interference (EMI). This implies that the traditional Gaussian noise model is no longer valid and an impulsive noise model has to be considered. Based on this observation, we investigate the performance of the max-dmin MIMO precoding technique, based on the minimum distance criterion, in an impulsive noise modeled as an α-stable distribution. The main contributions are (i) a general approximation of the error probability of the max-dmin precoder, in the presence of Cauchy noise for an n r ×n t MIMO system, and (ii) the performance evaluation, in terms of bit error rate, of a complete communication system, considering a MIMO channel model in tunnel and impulsive noise, both obtained by measurements. Two soft detection techniques, providing the soft decisions to the channel decoder, are proposed based on the approximation of the probability density function of the impulsive noise by either a Gaussian or a Cauchy law.

Analyses and Modeling Impulse Noise Generated by Household Appliances

This paper describes analysis of impulse noise generated by small household appliances. Furthermore we propose a new model of impulse noise based on the averaged power spectrum and the random phase generation with various phase distributions. The Gaussian, Weibull and Log-normal phase distributions were used to generate random phase. As a result of this approach, new impulses appear – they are different in the time domain but in the frequency domain new impulses have the desired power spectrum and the randomly generated phase.

A New Method for Impulse Noise Elimination and Edge Preservation

In this paper, a new method for impulsive noise reduction and edge preservation in images is presented. Images of different characteristics corrupted with a wide range of impulsive noise densities using two impulsive noise models are examined using the proposed method. In the detection stage of the method, two conditions have to be met to determine whether an image pixel is noisy or not. Two predetermined threshold values are involved in the computation of the second condition to differentiate between corrupted and uncorrupted pixels. Only pixels determined to be noisy in the detection stage are filtered in the next filtering stage where small size sliding windows are used to significantly reduce blurring effects in the output restored images. Several measuring indices have been used to examine the performance of the proposed method compared with many existing state-of-the-art methods in the literature of the image restoration field. Extensive simulation results show the superior performance of the proposed method over other techniques in terms of restoration quality, and preservation of images with fine details and edges.

A Markov-Middleton Model for Bursty Impulsive Noise: Modeling and Receiver Design

Transmission over channels impaired by impulsive noise, such as in power substations, calls for peculiar mitigation techniques at the receiver side in order to cope with signal deterioration. For these techniques to be effective, a reliable noise model is usually required. One of the widely accepted models is the Middleton Class A, which presents the twofold advantage to be canonical (i.e., invariant of the particular physical source mechanisms) and to exhibit a simple probability density function (PDF) that only depends on three physical parameters, making this model very attractive. However, such a model fails in replicating bursty impulsive noise, where each impulse spans over several consecutive noise samples, as usually observed (e.g., in power substations). Indeed, the Middleton Class A model only deals with amplitude or envelope statistics. On the other hand, for models based on Markov chains, although they reproduce the bursty nature of impulses, the determination of the suitable number of states and the noise distribution associated with each state can be challenging. In this paper, 1) we introduce a new impulsive noise model which is, in fact, a Hidden Markov Model, whose realizations exactly follow a Middleton Class A distribution and 2) we evaluate optimum and suboptimum detections for a coded transmission impaired by the proposed noise model.

A Blind Receiver with Multiple Antennas in Impulsive Noise Modeled as the Sub-Gaussian Distribution via the MCMC Algorithm

Receivers with an antenna array based on the assumption of Gaussian noise have experienced poor performance in extremely low-frequency/very-low-frequency (ELF/VLF) communication systems, in which the noise is highly impulsive. In this paper, a blind receiver with multiple antennas for channels with impulsive noise is developed to estimate signal and channel parameters jointly by using the Markov chain Monte Carlo (MCMC) algorithm. The impulsive noise is modeled as the sub-Gaussian distribution, which is widely applied. Simulation results show that the blind receiver can rapidly converge, and excellent performance can be achieved.

An intensity independent fixed valued impulse noise detector for image restoration

Most of the impulse noise detectors used for detection of fixed valued impulse noise are effective only for salt and pepper or a band type noise occurring at the extreme ends of the allowed range of intensity levels. The performance of these detectors deteriorates drastically when fixed valued impulses occur anywhere within the allowed gray scale. In this paper, an impulse detection scheme is proposed which can effectively detect all types of fixed valued impulse noise and also differentiates between noisy and noise-free pixels of identical intensity levels. The improved performance of the proposed method is verified through extensive simulations for various fixed valued impulse noise models.

Robust algorithm for broad impulse noise removal utilizing intensity distance and intensity height methodologies

In this manuscript, a new algorithm to reduce impulse noise from digital images has been proposed. This algorithm is based on switching median filtering approach, and therefore, it can be generally divided into two main stages; impulse noise detection stage and impulse noise cancellation stage. Modifications towards a well-known boundary discriminative noise detection method have been made. First, rather than using any sorting algorithm, we determine the local median values from manipulated local histograms. This solution makes the execution of the algorithm faster. Next, in the noise detection stage, in addition to the originally proposed intensity distance differential approach, the new method includes intensity height differential approach to reduce false detection rate. Then, instead of using adaptive approach in noise cancellation stage, our approach uses iterative approach, which has better local content preservation ability. Broad impulse noise model has been employed in this experiment. Based on the evaluations from root mean square error, false positive detection rate, false negative detection rate, mean structure similarity index, processing time, and visual inspection, it is shown that the proposed method is the best method when compared with seven other state-of-the-art median filtering techniques.

A Universal Impulse Noise Filter with an Impulse Detector and Nonlocal Means

In this paper, we propose an efficient filter for universal impulse noise removal. Operation is carried out in two stages: impulse detection followed by filtering. For detection, a robust local image statistic, called the extremum compression rank-order absolute difference (ECROAD), is designed to detect impulse noise in an image. For filtering, a universal impulse noise filter is proposed by combining the ECROAD statistic with the nonlocal means (NLM). The inherited switching behavior will preserve image details by selecting possible “noise pixels” for processing. Meanwhile, the joint impulsive weight is able to avoid the effect of impulsive components in restoring candidates. Simulation results show that the proposed filter produces excellent results and outperforms most existing filters for different impulse noise models.

Novel robust S transform based on the clipping method

This paper presents a novel robust S transform algorithm based on the clipping method to process signals corrupted by impulsive noise. The proposed algorithm is introduced to determine the clipping threshold value according to the characteristics of the signal samples. Signals in various impulsive noise models are considered to illustrate that the robust S transform can achieve better performance than the standard S transform. Moreover, mean square errors for instantaneous frequency estimation of the robust S transform are compared with that of the standard S transform, showing that the robust S transform can achieve significantly improved instantaneous frequency estimation for the signals in impulsive noise.

Impulsive Noise Mitigation in Powerline Communications Using Sparse Bayesian Learning

Additive asynchronous and cyclostationary impulsive noise limits communication performance in OFDM powerline communication (PLC) systems. Conventional OFDM receivers assume additive white Gaussian noise and hence experience degradation in communication performance in impulsive noise. Alternate designs assume a parametric statistical model of impulsive noise and use the model parameters in mitigating impulsive noise. These receivers require overhead in training and parameter estimation, and degrade due to model and parameter mismatch, especially in highly dynamic environments. In this paper, we model impulsive noise as a sparse vector in the time domain without any other assumptions, and apply sparse Bayesian learning methods for estimation and mitigation without training. We propose three iterative algorithms with different complexity vs. performance trade-offs: (1) we utilize the noise projection onto null and pilot tones to estimate and subtract the noise impulses; (2) we add the information in the data tones to perform joint noise estimation and OFDM detection; (3) we embed our algorithm into a decision feedback structure to further enhance the performance of coded systems. When compared to conventional OFDM PLC receivers, the proposed receivers achieve SNR gains of up to 9 dB in coded and 10 dB in uncoded systems in the presence of impulsive noise.

Variations on Impulse Noise Model in Digital Image Processing Field: A Survey on Current Research Inclination

As the information from digital images are easier to be evaluated as compared with one dimensional signals, digital images are now commonly used in may research fields. Unfortunately, similar to other digital signals, digital images are also sometimes unintentionally corrupted by unwanted signals, called noise. One of the noises commonly corrupting digital image is the impulse noise. Therefore, impulse noise reduction has become one of the active researches in these recent years. Many impulse noise models have been proposed by researchers for this research purpose. Therefore, the purpose of this paper is to investigate the popularity of these noise models. The research is done by a survey on available online materials. However, because there are more than thousands of related articles available online, the survey was carried out based on the keywords related to those articles. The research was restricted only to IEEExplore® database. The result from this survey shown that the research related to impulse noise model in digital image processing is still showing an increasing trend. Among the impulse noise models, the salt- and-pepper noise is the most used impulse noise model in current literature.

Total Variation Regularization Algorithms for Images Corrupted with Different Noise Models: A Review

Total Variation (TV) regularization has evolved from an image denoising method for images corrupted with Gaussian noise into a more general technique for inverse problems such as deblurring, blind deconvolution, and inpainting, which also encompasses the Impulse, Poisson, Speckle, and mixed noise models. This paper focuses on giving a summary of the most relevant TV numerical algorithms for solving the restoration problem for grayscale/color images corrupted with several noise models, that is, Gaussian, Salt & Pepper, Poisson, and Speckle (Gamma) noise models as well as for the mixed noise scenarios, such the mixed Gaussian and impulse model. We also include the description of the maximum a posteriori (MAP) estimator for each model as well as a summary of general optimization procedures that are typically used to solve the TV problem.

Bayesian Restoration of Audio Signals Degraded by Impulsive Noise Modeled as Individual Pulses

Impulsive noise, also known as clicks, is a very common type of distortion in old gramophone recordings. Existing methods (both heuristic and statistical) for removal of this type of defect usually do not exploit its underlying physical generation. This work proposes a model in which each click is individually modeled, which is more physically meaningful. A Bayesian method based on the reversible-jump Metropolis-Hastings algorithm for joint detection and removal of impulsive noise in audio signals is devised. Simulations with artificial and real audio signals as well as comparisons with competing approaches are presented to illustrate and validate the proposed method.

Robust Clipping for OFDM Transmissions over Memoryless Impulsive Noise Channels

The detriment arising from strong and frequently occurring impulses over an Orthogonal Frequency Division Multiplexing system is paramount because signals on sub-carriers appear to be corrupted simultaneously. To overcome this obstacle, clipping has been reported as an effective approach. Unlike previous works, this work derived the clipping threshold without assuming the a priori knowledge of the probability density function (PDF) of impulsive noise, which is usually unobtainable in precise measure in most practical scenarios, and may change rapidly over time. Then, a decoding metric accommodated to the clipping effect was derived to realize coding gain. To attest the proposed scheme, this study conducted computer simulations in compliance with the IEEE 1901 standard. For various impulse noise models under consideration, the proposed scheme was promisingly on par with its conventional counterpart, the clipping threshold of which, however, relies on an assumed PDF.

Impulse Noise Model and Its Variations

Impulse noise is one of the noise types that are normally corrupting digital images. In literature, impulse noises have been described in many ways. Therefore, the main aim of this manuscript is to survey a few impulse noise models that have been used by several researchers in digital image processing field. This will lead us to a better understanding on impulse noise models, and consequently will help the researchers to design more effective impulse noise reduction filters.