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Showing papers on "Impulse noise published in 1999"


Journal ArticleDOI
TL;DR: In this paper, a progressive switching median (PSM) filter is proposed to restore images corrupted by salt-pepper impulse noise, where an impulse detection algorithm is used before filtering, thus only a proportion of all the pixels will be filtered; and progressive methods are progressively applied through several iterations.
Abstract: A new median-based filter, progressive switching median (PSM) filter, is proposed to restore images corrupted by salt-pepper impulse noise. The algorithm is developed by the following two main points: 1) switching scheme-an impulse detection algorithm is used before filtering, thus only a proportion of all the pixels will be filtered; and 2) progressive methods-both the impulse detection and the noise filtering procedures are progressively applied through several iterations. Simulation results demonstrate that the proposed algorithm is better than traditional median-based filters and is particularly effective for the cases where the images are very highly corrupted.

1,012 citations


Journal ArticleDOI
TL;DR: A subspace-based technique for blind adaptive implementation of the robust multiuser detectors, which requires only the signature waveform and the timing of the desired user in order to demodulate that user's signal.
Abstract: In many wireless systems where multiuser detection techniques may be applied, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulsive phenomena. The performance of many multiuser detectors can degrade substantially in the presence of such impulsive ambient noise. We develop robust multiuser detection techniques for combating multiple-access interference and impulsive noise in CDMA communication systems. These techniques are based on the M-estimation method for robust regression. Analytical and simulation results show that the proposed robust techniques offer significant performance gain over linear multiuser detectors in impulsive noise, with little attendant increase in computational complexity. We also develop a subspace-based technique for blind adaptive implementation of the robust multiuser detectors, which requires only the signature waveform and the timing of the desired user in order to demodulate that user's signal. The robust multiuser detection technique and its blind adaptive version can be applied to both synchronous and asynchronous CDMA channels.

317 citations


Journal ArticleDOI
01 Aug 1999
TL;DR: Experimental results demonstrate that the proposed autofocusing technique outperforms existing techniques by enhancing the accuracy of the focus value of the video camera without the influence of noise.
Abstract: Most conventional autofocusing techniques based on the gradient estimator are very sensitive to noise. A new autofocusing technique which is resistive to noise generated by the CCD of video cameras is proposed. In the proposed scheme, the frequency selective weighted median (FSWM) filter is utilized to estimate the degree of focus and the fast hill-climbing search (HCS) strategy is exploited to determine the best focused image. Since the FSWM filter can not only extract high frequency components from the image, but also eliminate impulsive noise, the proposed autofocusing method employing the FSWM criterion function can estimate the degree of focus precisely. Furthermore, the proposed real-time HCS algorithm enables the video camera to continuously focus on dynamic images. Experimental results demonstrate that the proposed technique outperforms existing techniques by enhancing the accuracy of the focus value of the video camera without the influence of noise.

193 citations


Journal ArticleDOI
F. Russo1
TL;DR: A new family of filters for images corrupted by impulse noise and a new class of noise-protected operators for edge detection that perform significantly better than other techniques in the literature are presented.

156 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present the results of a study covering measurement and characterization of the wide-band impulsive noise present in a digital TV radio channel, where the measurements were conducted at a frequency of 762 MHz in different outdoor and indoor environments using vertical and horizontal polarization.
Abstract: This paper presents the results of a study covering measurement and characterization of the wide-band impulsive noise present in a digital TV radio channel. Measurements were conducted at a frequency of 762 MHz in different outdoor and indoor environments using vertical and horizontal polarization. The measurement system was built on commercial equipment only. The calibration process, which is an important stage of this kind of measurements, is described. To analyze the measurements the impulsive noise has been modeled as a pulse train where the pulse amplitude, pulse duration and elapsed time between pulses are considered random variables. It has been found that the pulse duration and elapsed time between pulses is not dependent on the antenna polarization while the pulse amplitude is, especially in the case of the noise generated by a fluorescent lamp. It has also been found that the pulse duration of the noise measured in the outdoor environments presents some clustering features and is correlated with the pulse amplitudes. This correlation may be caused by a RF noise bandwidth that is larger than the bandwidth of the measurement system. The noise in busy streets presents larger pulse durations, larger amplitude, and shorter elapsed time between pulses that the noise measured in a pedestrian area. Several statistical tests have been done to find the distribution function that best fits these random variables. Power Rayleigh, lognormal, exponential, Poisson, and Gamma distributions have been tested. According to the assessment carried out, none of the distribution functions is adequate to model the pulse amplitudes or the elapsed time between pulses, while the pulse duration seems to be Gamma distributed.

135 citations


Patent
15 Jan 1999
TL;DR: In this paper, an impulse noise detector detects impulse noise in an audio signal by filtering out the audio components of the signal, then comparing an envelope of a filtered signal with a threshold obtained as a moving average of the envelope.
Abstract: An impulse noise detector detects impulse noise in an audio signal by filtering out the audio components of the signal, then comparing an envelope of a filtered signal with a threshold obtained as a moving average of the envelope. Short-duration impulse noise is thereby detected without detecting tone bursts and other fast-rising signals of longer duration. The envelope may be taken directly from the filtered signal, or from a difference signal obtained from a preliminary envelope of the filtered signal, to emphasize impulse noise when distorted audio components leak into the filtered signal.

66 citations


Patent
09 Sep 1999
TL;DR: In this article, the authors proposed a system for digital communications over channels that suffer from impulse noise, and particularly over return cable TV channels, downstream cable TV channel, and digital subscriber loops (DSL) channels for high speed communications over twisted pair copper lines.
Abstract: This invention is particularly useful as a system for digital communications over channels that suffer from impulse noise, and particularly over return cable TV channels, downstream cable TV channels, and digital subscriber loops (DSL) channels for high speed communications over twisted pair copper lines.

57 citations


Journal ArticleDOI
F. Russo1
TL;DR: Experimental results show that the neuro-fuzzy filter is able to yield a very effective noise cancellation and to perform significantly better than state-of-the-art operators in the literature.

44 citations



Journal ArticleDOI
TL;DR: It is shown that the normalized least mean p-norm (NLMP) and Douglas' family of normalized leastmean square algorithms are special cases of the proposed class of algorithms for finite impulse response adaptive filtering.
Abstract: A new class of algorithms based on the fractional lower order statistics is proposed for finite impulse response adaptive filtering in the presence of a stable processes. It is shown that the normalized least mean p-norm (NLMP) and Douglas' family of normalized least mean square algorithms are special cases of the proposed class of algorithms. A convergence proof for the new algorithm is given by showing that it performs a descent-type update of the NLMP cost function. Simulation studies indicate that the proposed algorithms provide superior performance in impulsive noise environments compared to the existing approaches.

37 citations


Journal ArticleDOI
TL;DR: In this article, the amplitudes of electromagnetic vehicle ignition noise were made in Ottawa at six fixed frequencies in the range from 150 to 500 MHz using a 10 kHz bandwidth, and statistical analyses were performed of both the amplitude and temporal characteristics of the impulsive noise.
Abstract: Temporal sweeps of the amplitudes of electromagnetic vehicle ignition noise were made in Ottawa at six fixed frequencies in the range from 150 to 500 MHz using a 10 kHz bandwidth. Statistical analyses were performed of both the amplitude and temporal characteristics of the impulsive noise. The amplitudes approximately followed a lognormal distribution. The pulse spacings were uniformly distributed between about 5 and 15 ms and the pulse durations were about 150 /spl mu/s long.

Proceedings ArticleDOI
21 May 1999
TL;DR: An adaptive median filter algorithm to remove impulse noise in x-ray images and speckle in ultrasound images is presented, which considers the local variability over the entire image to ensure that the fine details are preserved and more than 90 percent of the original information is retained.
Abstract: An adaptive median filter algorithm to remove impulse noise in x-ray images and speckle in ultrasound images is presented. The ordinary median filter tends to distort or lose fine details in an image. Also, a significant amount of the original information in the image is altered. The proposed algorithm considers the local variability over the entire image to ensure that the fine details are preserved and more than 90 percent of the original information is retained. The robustness of the algorithm is demonstrated by applying it to images from different modalities like diagnostic x-ray, CT, portal imaging and ultrasound.

Journal ArticleDOI
TL;DR: Experimental results show that the proposed approach is very effective also in the presence of data highly corrupted by noise and largely able to outperform other methods in the literature including state-of-the-art techniques.
Abstract: A new class of neural fuzzy filters for removing noise from two-dimensional (2-D) measurement data is presented. The proposed approach combines the advantages of the fuzzy and neural paradigms. The network structure is, in fact, specifically designed to exploit the effectiveness of fuzzy reasoning in removing noise without destroying the useful information embedded in the input data. An easy design of new filters is thus obtained because the neuro-fuzzy approach is capable of automatic acquisition of knowledge for a given network structure. The learning method based on genetic algorithms performs an effective training of the network yielding satisfactory results after a few generations. Experimental results show that the proposed approach is very effective also in the presence of data highly corrupted by noise. The neural fuzzy system is largely able to outperform other methods in the literature including state-of-the-art techniques.

Proceedings ArticleDOI
15 Mar 1999
TL;DR: In this article, a FIR adaptive equaliser for impulse noise suppression is proposed based on the minimization of an M-estimate objective function which has the ability to ignore or down-weight a large error signal when it exceeds certain thresholds.
Abstract: In this paper, a FIR adaptive equaliser for impulse noise suppression is proposed. It is based on the minimization of an M-estimate objective function which has the ability to ignore or down-weight a large error signal when it exceeds certain thresholds. An advantage of the proposed method is that its solution is governed by a system of linear equations, called the M-estimate normal equation. Therefore, traditional fast algorithms like the recursive least squares algorithm can be applied. Using a robust estimation of the thresholds and the recursive least square algorithm, an M-estimate RLS (M-RLS) algorithm is developed. Simulation results show that the proposed algorithm has better convergence performance than the N-RLS and MN-LMS algorithms when the input signal of the equaliser is corrupted by individually or consecutive impulse noises. It also shares the low steady state error of the traditional RLS algorithm.

01 Jan 1999
TL;DR: In this article, the efficiency of temporal and spatial adaptive techniques for impulsive noise mitigation was analyzed for surface wave over-the-horizon radars, especially ones located in tropical areas, such as Northern Australia, and it was shown that for heavily contaminated dwells, new spatio-temporal adaptive processing is most effective.
Abstract: : Surface-wave over-the-horizon radars, especially ones located in tropical areas, such as Northern Australia, are usually strongly affected by external impulsive noise. Apart from thunderstorm activity, man-made (industrial) noise over typically quite long coherent-integration time often is of impulsive nature as well. In this paper we analyse the efficiency of temporal and spatial adaptive techniques for impulsive noise mitigation. We demonstrate that for heavily contaminated dwells, new spatio-temporal adaptive processing is most effective. Initial impulsive noise mitigation, produced by adaptive spatial processing is used for range and azimuth dependent sea-clutter spectrum estimation. Estimated sea-clutter spectrum is then used to 'restore' the 'missing' data, originally contaminated by impulsive noise.

Proceedings ArticleDOI
15 Mar 1999
TL;DR: A general expression for the Cramer-Rao bound (CRB) for direction finding is developed using arrays for deterministic signals plus i.i.d. non-Gaussian noise, generalizing the Gaussian CRB.
Abstract: We consider narrowband angle of arrival estimation in non-Gaussian (NG) noise channels, such as arises in some indoor and outdoor mobile communications channels We develop a general expression for the Cramer-Rao bound (CRB) for direction finding using arrays for deterministic signals plus iid non-Gaussian noise, generalizing the Gaussian CRB The CRBs for the noise and direction parameters decouple The CRB for direction finding is expressed as a product of two terms that depend on the noise distribution, and the signal, respectively We illustrate the results for a Gaussian mixture PDF, and present simulation results comparing five direction finding algorithms An approach based on the expectation-maximization (EM) algorithm, that simultaneously estimates the noise parameters, the signal directions, and the signal waveforms, is shown to achieve the CRB over a wide SNR range

Journal ArticleDOI
TL;DR: AWFM is an extension of the weighted fuzzy mean (WFM) filter to overcome the drawback of WFM in fine signal preservation and not only preserves the high performance of W FM on heavy additive impulse noise, but also improves the efficiency of Wfm on removing light additive impulse Noise.
Abstract: The important properties and applications of the adaptive weighted fuzzy mean (AWFM) filter are presented in this paper. AWFM is an extension of the weighted fuzzy mean (WFM) filter to overcome the drawback of WFM in fine signal preservation. It not only preserves the high performance of WFM on heavy additive impulse noise, but also improves the efficiency of WFM on removing light additive impulse noise. Some deterministic and statistical properties of the AWFM filter are analyzed, and the main characteristic of the AWFM filter that maps the input signal space into a root signal space, where a root signal is an invariant signal to the filter, is also discussed. Compared with the other filters, AWFM exhibits better performance in the criteria of mean absolute error and mean square error. On the subjective evaluation of those filtered images, AWFM also results in a higher quality of global restoration. ©1999 John Wiley & Sons, Inc.


Proceedings ArticleDOI
24 Oct 1999
TL;DR: A Video-Data Dependent Weighted Average (Video-DDWA) filter for image sequence restoration degraded by additive Gaussian noise and is proven to be more effective both the restoration results and computation time than the 3D-DDWM filter with impulse robust MC for removing mixed noise from image sequence.
Abstract: In this study, we consider a filtering method for image sequence degraded by additive Gaussian noise and/or impulse noise (i.e., mined noise). In general, for the image sequence filtering, motion compensation (MC) method is required in order to obtain good filtering performance both in the still and moving regions of an image sequence. Nevertheless a heavy computation load is imposed on MC method and MC tends to get mistaken motion vector owing to additive noise. To overcome above drawbacks of MC, we have proposed a Video-Data Dependent Weighted Average (Video-DDWA) filter for image sequence restoration degraded by additive Gaussian noise. The Video-DDWA filter whose weights are controlled by some local information contain a motion information as a motion detector is shown that the motion information method is more effective tool than MC method for image sequence restoration. However Video-DDWA filter is not proper for removing the mixed noise. Therefore, we replace weighted average filters and a motion information of the Video-DDWA with weighted median filters and a mixed noise robust motion information, respectively. We propose this filter as a Video-Data Dependent Weighted Median (Video-DDWM) filter for removing mixed noise from image sequence. Through some simulations, the Video-DDWM filter is proven to be more effective both the restoration results and computation time than the 3D-DDWM filter with impulse robust MC for removing mixed noise from image sequence.

Proceedings ArticleDOI
31 Oct 1999
TL;DR: It is shown that when non-Gaussian impulsive noise is present, the FRESH filter is still effective against interference, even when the two signals have cyclic frequencies in common, but if hole-punching is used to remove the larger impulses of the noise, this adversely affects the performance of theFRESH filter.
Abstract: The use of frequency-shift (FRESH) filtering for the rejection of adjacent channel interference (ACI) in GMSK modulated VLF communications is investigated in the presence of impulsive noise. The effects of such filtering in conjunction with a simple "hole-punching" technique for removing impulses from the signal are characterised. A range of realistic scenarios based on a high powered GMSK interferer (10 to 30 dB greater than the signal of interest (SOI)) in an adjacent channel are described. It is known that in the presence of interference and Gaussian noise a simple FRESH filter, which exploits the cyclostationarity of the interferer, is highly effective at removing the interference. We show that when non-Gaussian impulsive noise is present, the FRESH filter is still effective against interference, even when the two signals have cyclic frequencies in common. However if hole-punching is used to remove the larger impulses of the noise, this adversely affects the performance of the FRESH filter.

Proceedings ArticleDOI
15 Mar 1999
TL;DR: This paper addresses the problem of blind equalization for digital communications using an array of sensors at the receiver to copy constant modulus signals in the presence of heavy-tailed additive channel noise by introducing a new CMA criterion based on the fractional lower-order statistics of the received data.
Abstract: This paper addresses the problem of blind equalization for digital communications using an array of sensors at the receiver to copy constant modulus signals in the presence of heavy-tailed additive channel noise. First, we demonstrate the negative effects of channel noise to the original constant modulus algorithm (CMA) cost function in terms of convergence. Then, we introduce a new CMA criterion based on the fractional lower-order statistics (FLOS) of the received data. The proposed criterion is able to mitigate impulsive noise at the receiver and at the same time restores the constant modulus character of the transmitted communication signal. We perform an analytical study of the properties of the new cost function and we illustrate its convergence behavior through computer simulations.

Journal ArticleDOI
TL;DR: The probability density functions of the amplitude, duration, and inter-arrival time of impulse noise recently derived in a study carried out in the German Telephone Network are used to obtain a simple closed form expression for estimating the bit error rate performance of data transmission in digital subscriber loops.
Abstract: The probability density functions of the amplitude, duration, and inter-arrival time of impulse noise recently derived in a study carried out in the German Telephone Network are used to obtain a simple closed form expression for estimating the bit error rate performance of data transmission in digital subscriber loops.

Journal ArticleDOI
TL;DR: An error probability analysis for the DMT-based DSL in presence of additive white Gaussian noise, impulse noise (IN) and crosstalk is presented and a closed-form expression for the error probability performance of the D MT system with Quadrature Amplitude Modulation (QAM) modulation is derived.
Abstract: The transmission of high-speed data over Digital Subscriber Loop (DSL) can be accomplished through the use of Discrete Multitone (DMT). Due to the frequency dependent channel distortion and crosstalk, there is a need to determine the performance of DMT-based DSL for system optimization purpose. This paper presents an error probability analysis for the DMT-based DSL in presence of additive white Gaussian noise (AWGN), impulse noise (IN) and crosstalk. The bandlimitation effect of the DSL on the DMT signal is studied based on the discrete impulse response of the channel. Impairments after Fourier transformation at the receiver end are analysed. A recently proposed impulse noise model, in which IN is viewed as the product of a Bernoulli process and a Gaussian process is adopted. Crosstalk noise is assumed to be Gaussian distributed with its variance determined from the frequency response of the DSL and empirically obtained coupling constants. A closed-form expression for the error probability performance of the DMT system with Quadrature Amplitude Modulation (QAM) modulation is derived.

Journal ArticleDOI
TL;DR: An improved 2-D median filter employing multishell concept to recover missing lines and to suppress impulse noise, which reduces the number of replacement and results in better performance and simple hardware realization.
Abstract: An improved 2-D median filter employing multishell concept to recover missing lines and to suppress impulse noise, is presented. The performance of proposed filter is evaluated over image 'LENA'. The impulsive noise is added using MATLAB utility. The modified strategy reduces the number of replacement and results in better performance and simple hardware realization.


Proceedings ArticleDOI
15 Mar 1999
TL;DR: A method for restoring missing samples in digital signals using a Markov Chain Monte Carlo approach and an introduction to these numerical techniques is given.
Abstract: Summary form only given. This paper outlines a method for restoring missing samples in digital signals. The missing samples are imputed using a Markov Chain Monte Carlo approach and an introduction to these numerical techniques is given. One application area is presented from the area of digital audio restoration where clicks are a familiar problem, and can take the form of sudden unexpected bursts of impulsive noise with random but finite duration. These bursts of noise have numerous causes such as dirt, electrical interference or mechanical damage to the storage medium. The original signal is often effectively lost. Several methods of detecting clicks have been devised, with the best approaches being model based. Once a click has been detected the "suspect" samples are removed and replaced by interpolation. Results obtained on both synthetic and real data are given.

Patent
10 Mar 1999
TL;DR: Distortion discrimination circuitry for digital radio receivers and corresponding methods are disclosed that accurately and efficiently discriminate distortion events including impulse noise and multipath distortion events, to improve the quality of audio output signals as discussed by the authors.
Abstract: Distortion discrimination circuitry for digital radio receivers and corresponding methods are disclosed that accurately and efficiently discriminate distortion events, including impulse noise and multipath distortion events, to improve the quality of audio output signals. The distortion discrimination circuitry monitors and analyzes the demodulator output to determine when a distortion event has occurred and provides an appropriate indication signal for use by other circuitry within the radio receiver. More particularly, the distortion discrimination circuitry includes impulse noise circuitry that looks for high frequency noise in both the magnitude and multiplexed outputs of the demodulator to determine the occurrence of impulse noise distortion events. The distortion discrimination circuitry also includes multipath circuitry that looks for a drop-off in signal power between the multiplexed output of the demodulator and a moving average version of that same signal to determine the occurrence of multipath distortion events. In addition, stereo decoder circuitry modifies the audio output signals in response to indications of distortion events.

01 Jan 1999
TL;DR: Worker exposure to noise on high-rise construction sites is an ever-present hazard and one that is commonly accepted by many industry workers as discussed by the authors, however, the potential risk to the individual through repeated exposure to excessive noise on these projects is very real, concerning but controllable.
Abstract: Worker exposure to noise on high-rise construction sites is an ever-present hazard and one that is commonly accepted by many industry workers. The potential risk to the individual through repeated exposure to excessive noise on these projects is very real, concerning but controllable. This study focuses on establishing a risk profile on workers exposed to excessive noise including the identification of highrisk operational areas and work activities influential in affecting worker exposure. Involved were 238 workers from 20 occupational groups who were personally monitored for noise exposure during the construction of three high rise projects on the Gold Coast, Queensland. The study results clearly showed that high-rise construction workers are exposed to high levels of impact and steady state noise during work. In particular, occupational groups such as formwork carpenters (93.52 dB(A)), concreters (93.5 dB(A)), concrete line hand operators (92.97 dB(A)), formwork labourers (91.78 dB(A)), scaffolders (91.7 dB(A)), internal carpenters (91.41 dB(A)) and dogman (90.80 dB(A)) were identified as high risk exposure groups. As defined in Queensland legislation, noise exposure criteria represents an eight hour equivalent continuous A-weighted sound pressure level, LAeq, 8hr of 85 dB(A) or in the case of exposure to instantaneous noise levels a linear (unweighted peak) peak sound pressure level, Lpeak, 140 dB(lin). Eight hundred and twenty nine workers (N-829) also participated in the questionnaire survey. The responses were varied; however, there was a direct correlation between personal dosimetry results in certain occupations and their perception on their current state of hearing. A high proportion of workers 644 (77.7%) have not undergone audiometric testing and 203 (30.3%) of the subjects indicated having symptoms of tinnitus (ringing in the ears). Noise emanating from machinery, tools and activities i.e. tower cranes, hammer drills, circular saws, dropping of materials and impulse noise from explosive power tools are just some of the noise sources characteristic of construction work. Machoism, worker apathy, lack of industry self-regulation and organisational deficiencies in effectively managing noise and hearing conservation issues were identified as some of the major shortcomings prevalent within the industry. Although sophisticated technology has been devised to measure and control noise and minimise its impact within many industries, there is a lack of documented research into the state of noise and hearing conservation on high-rise construction sites specifically. In conclusion, there is a case for more stringent noise exposure controls on these projects including the role and function of hearing conservation programs, including audiometric screening of workers, assessing risk and control of noise through engineering noise reduction. This paper briefly discusses the research findings following an eight-month study into noise within the high-rise construction industry.

Journal ArticleDOI
TL;DR: In this paper, the impact of phase noise introduced by bit and symbol timing mechanism is discussed and a pilot correction and the cyclic prefix protection method are put forward to deal with the problem.
Abstract: OFDM (the orthogonal frequency division multiplexing) and its variety DMT (the discrete multitone) as delegates of the multicarrier modulation technology have given a big impact on the conventional data communication applications. Based on the theoretic a analysis of the OFDM technology, the impact of phase noise that introduced by the bit and symbol timing mechanism is discussed. Then a pilot correction and the cyclic prefix protection method are put forwarded to deal with the problem. These methods have been used in our experimental OFDM cable modem system to cope with the impulse noise and narrow band interference in the HFC (hybrid fiber and coax) upstream channel.

Proceedings ArticleDOI
TL;DR: A probabilistic model is presented for the SD-ROM filter that characterizes the performance of the algorithm in terms of the probability of detecting a corrupted pixel while avoiding uncorrupted pixels and applies the insight gained to optimized thresholds found using a computerized search algorithm for a large number of images and noise conditions.
Abstract: One well-studied image processing task is the removal of impulse noise from images. Impulse noise can be introduced during image capture, during transmission, or during storage. The signal-dependent rank order mean (SD-ROM) filter has been shown to be effective at removing impulses from 2-D scalar- valued signals. Excellent results were presented for both a two-state and a multi-state version of the filter. The two- state SD-ROM filter relies on the selection of a set of threshold values. In this paper, we examine the performance of the algorithm with respect to the thresholds. We take three different approaches. First, we discuss the performance of the algorithm with respect to its root signals. Second, we present a probabilistic model for the SD-ROM filter. This model characterizes the performance of the algorithm in terms of the probability of detecting a corrupted pixel while avoiding uncorrupted pixels. Finally, we apply the insight gained from the root signal analysis and the statistical model to optimized thresholds found using a computerized search algorithm for a large number of images and noise conditions.