Noise Probability Research Articles

Real-Time Color Imaging Based on RM-Filters for Impulsive Noise Reduction

In this article, we propose a new class of multichannel filters, vector rank M-type K-nearest neighbor (VRMKNNF) filters that can obtain the balance between noise suppression, and edge and fine detail preservation, especially in color image restoration. The proposed VRMKNNF filters are mainly based on the combined RM-estimators with different influence functions. An adaptive non parametric approach that determines the functional form of the density probability of noise from data into the sliding filtering window has been employed to improve the performance of the multichannel filters. Applying the VRMKNNF as a reference filter we designed the adaptive multichannel non parametric VRMKNNF (AMN-VRMKNNF). Numerous simulations presented in the article illustrate that the VRMKNNF and AMN-VRMKNNF filters exhibit the robust and adaptive capability in multichannel imaging applications. Finally, we present the implementation of proposed filters on the DSP TMS320C6711 demonstrating that they can potentially provide a real-time solution to quality video transmission.

Quantization Error and Resolution in Ensemble Averaged Data With Noise

We investigate the properties of ensemble averaged data from a uniform quantizer, when the quantizer input signal is noisy. An expression for the mean-square error (MSE) MSE(/spl sigma/,N) of the ensemble averaged data, accounting for an ensemble of finite length N, and noise RMS /spl sigma/, is obtained. Previously published results for N=1 and N/spl rarr//spl infin/ are recovered. For intermediate N, we show that there is an optimal noise RMS, /spl sigma//sub opt/(N), which minimizes the MSE. Such a minimum point exists regardless of the type of noise probability distribution function. Conditions on /spl sigma/ and N for achieving a smaller MSE than in the noise-free case (/spl Delta//sup 2//12) are discussed. The convergence properties of MSE(/spl sigma/,N) for increasing N, and the effect of applying uniformly distributed dither, is established.

Image Denoising by Statistical Area Thresholding

Area openings and closings are morphological filters which efficiently suppress impulse noise from an image, by removing small connected components of level sets. The problem of an objective choice of threshold for the area remains open. Here, a mathematical model for random images will be considered. Under this model, a Poisson approximation for the probability of appearance of any local pattern can be computed. In particular, the probability of observing a component with size larger than k in pure impulse noise has an explicit form. This permits the definition of a statistical test on the significance of connected components, thus providing an explicit formula for the area threshold of the denoising filter, as a function of the impulse noise probability parameter. Finally, using threshold decomposition, a denoising algorithm for grey level images is proposed.

Calculation of bit-error rates and power penalties due to incoherent crosstalk in optical networks using Taylor series expansions

A new calculation method is presented for bit-error rates and power penalties due to incoherent crosstalk from up to eight interferers of different powers, based on a truncated Taylor series approximation of the crosstalk contribution to the noise probability density function. Formulae are provided for bit-error rates and power penalties in both thermal and ASE limited systems, with average-power and optimized decision thresholds, and include extinction ratio effects. The technique forms an excellent complement to the Gaussian approximation.

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Noise can improve how memoryless neurons process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect at the level of threshold neurons and continuous neurons. This paper presents theoretical and simulation evidence that 1) lone noisy threshold and continuous neurons exhibit the SR effect in terms of the mutual information between random input and output sequences, 2) a new statistically robust learning law can find this entropy-optimal noise level, and 3) the adaptive SR effect is robust against highly impulsive noise with infinite variance. Histograms estimate the relevant probability density functions at each learning iteration. A theorem shows that almost all noise probability density functions produce some SR effect in threshold neurons even if the noise is impulsive and has infinite variance. The optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases. Simulations further show that the SR effect persists for several sigmoidal neurons and for Gaussian radial-basis-function neurons.

On the Discreteness of Capacity-Achieving Distributions

We consider a scalar additive channel x /spl rarr/ x + N whose input is amplitude constrained. By extending Smith's (1969) argument, we derive a sufficient condition on noise probability density functions (pdf) that guarantee finite support for the associated capacity-achieving distribution(s).

Robust stochastic resonance for simple threshold neurons

Simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic-resonance or SR effect. Input-output mutual information measures the performance of such threshold systems that use subthreshold signals. The SR result holds for all possible noise probability density functions with finite variance. The only constraint is that the noise mean must fall outside a "forbidden" threshold-related interval that the user can control--a new theorem shows that this condition is also necessary. A corollary and simulations show that the SR effect occurs for right-sided beta and Weibull noise as well. These SR results further hold for the entire uncountably infinite class of alpha-stable probability density functions. Alpha-stable noise densities have infinite variance and infinite higher-order moments and often model impulsive noise environments. The stable noise densities include the special case of symmetric bell-curve densities with thick tails such as the Cauchy probability density. The SR result for alpha-stable noise densities shows that the SR effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise. Regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell-curve tail thickness and an approximate linear relationship for the SR-maximal mutual information as a function of the alpha bell-curve tail thickness.

Detail preserving impulsive noise removal

Most image processing applications require noise elimination. For example, in applications where derivative operators are applied, any noise in the image can result in serious errors. Impulsive noise appears as a sprinkle of dark and bright spots. Transmission errors, corrupted pixel elements in the camera sensors, or faulty memory locations can cause impulsive noise. Linear filters fail to suppress impulsive noise. Thus, non-linear filters have been proposed. Windyga's peak-and-valley filter, introduced to remove impulsive noise, identifies noisy pixels and then replaces their values with the minimum or maximum value of their neighbors depending on the noise (dark or bright). Its main disadvantage is that it removes fine image details. In this work, a variation of the peak-and-valley filter is proposed to overcome this problem. It is based on a recursive minimum–maximum method, which replaces the noisy pixel with a value based on neighborhood information. This method preserves constant and edge areas even under high impulsive noise probability. Finally, a comparison study of the peak-and-valley filter, the median filter, and the proposed filter is carried-out using different types of images. The proposed filter outperforms other filters in the noise reduction and the image details preservation. However, it operates slightly slower than the peak-and-valley filter.

A new equal-partition measurement encoding scheme for networked control systems

In this paper, a new encoding strategy is proposed for data exchange through limited bandwidth communication networks. The proposed strategy belongs to the family of finitely recursive equal-partition schemes. Convergence results are proposed under bounded measurement noises. When the noise probability density function is known, heuristic procedure is proposed to optimize the encoding scheme’s parameters. This is done using the discrete-time Markov chains tool. Simulations may be viewed at http://www.lag.ensieg.inpg.fr/alamir/Network.electrics/alamir_commault.pdf

Stochastic Properties of Quantization Noise in Memoryless Converters Affected by Integral Nonlinearity

This paper is focused on the stochastic properties of quantization noise introduced by nonideal memoryless converters. In particular, overloading effects and integral nonlinearity (INL) are considered. A theoretical model is given, which accurately describes the quantization noise probability density function in presence of overloading noise and both deterministic and stochastic INL. A Gaussian stimulus is adopted for validation purposes due to its relevance in modern telecommunication systems. The proposed model is then used to derive quantization noise power as a function of both input signal and INL stochastic properties, in order to evaluate the average performance of classes of analog-to-digital converters (ADC). Finally, the results are applied to a memoryless converter affected by Gaussian INL, analyzing the properties of quantization noise.

Performance of laser tracking of small targets during turbulence and beam jitter

Small target detection and tracking are important for laser radars in many applications such as laser weapons, directed infrared countermeasures (DIRCM), fire control, target recognition, and free-space laser communications. The detection and tracking performance depends on the mode of detection, SNR, target signal statistics, beam jitter, and turbulence induced irradiance variations. We show results of the root mean square (rms) tracking error versus SNR primarily for direct detection systems using a strong glint return. For the general case of a certain signal and noise probability density functions (pdf) it is hard to obtain analytical solutions for the mean and variances of the estimates for the rms tracking error. We have therefore used numerical simulations to illustrate how the pdf and SNR will affect the tracking accuracy. Gamma functions and other pdf's can be used to characterize the signal distributions to get a first hand on tracking performance. The results are presented as tracking errors versus the angular spot size of the laser beam in the tracking detector plane. We also investigate the beam optimization problem for target detection and "power in bucket," which is maximizing the laser energy at the target. We find that there are optimum beam sizes (w) versus the rms jitter () and that optimum w/ (minimizing the false alarm rate for a given detection probability Pd) typically fall in regions 1 to 3 depending on probability of detection and the representative pdf for the application in mind.

Maximum entropy decomposition of quadrupole mass spectra

We present an information-theoretic method called generalized maximum entropy (GME) for decomposing mass spectra of gas mixtures from noisy measurements. In this GME approach to the noisy, underdetermined inverse problem, the joint entropies of concentration, cracking, and noise probabilities are maximized subject to the measured data. This provides a robust estimation for the unknown cracking patterns and the concentrations of the contributing molecules. The method is applied to mass spectroscopic data of hydrocarbons, and the estimates are compared with those received from a Bayesian approach. We show that the GME method is efficient and is computationally fast.

Noise and Regeneration in Semiconductor Waveguides With Saturable Gain and Absorption

We have modeled the noise properties of a novel waveguide device with regenerative properties. The device consists of alternating sections of saturable gain and absorption, which give a nonlinear power transfer function. We investigate the relative intensity noise spectra and signal-to-noise ratio after the device by both a small-signal analysis and large-signal simulation, and we show that the gain saturation gives noise redistribution at the mark level. We also examine the influence of the nonlinearity on the noise probability density function and show that the standard approximations of Gaussian and noncentral /spl chi//sup 2/ distributions do not give a satisfying description. The strength and weaknesses of the limiting cases of static transfer functions and linear noise transfer as well as the small-signal analysis are examined in the case of bit-error-rate estimation in a cascade of regenerators. The interplay between increased nonlinearity and noise is investigated and we show that the increased nonlinearity achieved by additional device sections can improve the cascadability although more amplified spontaneous emission noise is added.

Ultrasonic flaw detection in NDE of highly scattering materials using wavelet and Wigner–Ville transform processing

In ultrasonic non-destructive evaluation of highly scattering materials the backscattering noise may attain peak values greater than the searched flaw pulse and the mean value of noise spectrum is very similar to the searched echo spectrum. Several specific methods have been proposed for the reduction of this type of noise, but the comparison of the performance of different methods is still an open problem. In this paper, we make a comparison among some methods based on simultaneous representations in time and frequency/scale domains of the ultrasonic traces. Synthetic and experimental traces are de-noised using a discrete wavelet processor with decomposition level-dependent threshold selection and a method that combines Wigner–Ville transform and filtering in the time–frequency domain. The results are comparatively evaluated in terms of signal to noise ratio and probability of detection.

Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates

Feedback control with limited data rates is an emerging area which incorporates ideas from both control and information theory. A fundamental question it poses is how low the closed-loop data rate can be made before a given dynamical system is impossible to stabilize by any coding and control law. Analogously to source coding, this defines the smallest error-free data rate sufficient to achieve "reliable" control, and explicit expressions for it have been derived for linear time-invariant systems without disturbances. In this paper, the more general case of finite-dimensional linear systems with process and observation noise is considered, the object being mean square state stability. By inductive arguments employing the entropy power inequality of information theory, and a new quantizer error bound, an explicit expression for the infimum stabilizing data rate is derived, under very mild conditions on the initial state and noise probability distributions.

White noise analysis for Lévy processes

We construct a white noise theory for Lévy processes. The starting point of this theory is a chaos expansion for square integrable random variables. We use this approach to Malliavin calculus to prove the following white noise generalization of the Clark–Haussmann–Ocone formula for Lévy processes F(ω)=E[F]+ ∑ m⩾1 ∫ 0 T E[D t (m)F| F t]♢ Y • t (m) dt. Here E[ F] is the generalized expectation, the operators D t ( m) F, m⩾1 are (generalized) Malliavin derivatives, ♢ is the Wick product and for all m⩾1 Y • t (m) is the white noise of power jump processes Y t ( m) . In particular, Y • t (1) is the white noise of the Lévy process. The formula holds for all F∈ G ∗⊃L 2(μ) , where G ∗ is a space of stochastic distributions and μ is a white noise probability measure. Finally, we give an application of this formula to partial observation minimal variance hedging problems in financial markets driven by Lévy processes.

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II. Bayesian analyses

In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in weak signal limit. For stochastic signals, the resulting statistic consisted of a sum of an auto-correlation term and a cross-correlation term; it was necessary to discard by hand the auto-correlation term to obtain the correct, generalized cross-correlation statistic. In the present paper, we present an alternative Bayesian derivation of the same signal detection techniques. We compute the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the integrated signal-to-noise ratio is large compared to one, and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in the previous paper. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic auto-correlation term.

Stochastic resonance in noisy threshold neurons

Stochastic resonance occurs when noise improves how a nonlinear system performs. This paper presents two general stochastic-resonance theorems for threshold neurons that process noisy Bernoulli input sequences. The performance measure is Shannon mutual information. The theorems show that small amounts of independent additive noise can increase the mutual information of threshold neurons if the neurons detect subthreshold signals. The first theorem shows that this stochastic-resonance effect holds for all finite-variance noise probability density functions that obey a simple mean constraint that the user can control. A corollary shows that this stochastic-resonance effect occurs for the important family of (right-sided) gamma noise. The second theorem shows that this effect holds for all infinite-variance noise types in the broad family of stable distributions. Stable bell curves can model extremely impulsive noise environments. So the second theorem shows that this stochastic-resonance effect is robust against violent fluctuations in the additive noise process.

Phase noise analysis of the OFDM communication system by the standard frequency deviation

This paper analyzes phase noise effects on the performance of an OFDM communication system by the linear approximation approach. We newly present a generalized phase noise power spectrum density (PSD) model using the normalized phase noise power spectrum model-Lorentzian model. Also, we derive the relationship between the phase noise PSD's parameter f/sub 3dB/ and the standard frequency deviation f/sub d/ of phase noise probability density function (PDF), and the relationship between phase noise variance /spl sigma//sub /spl phi///sup 2/ and f/sub d/. Analytical BER results closely match with simulation results of the OFDM communication system using QPSK and 16QAM modulation format. The performance of OFDM system is evaluated when the bandwidth B/sub s/=10 MHz and phase noise is included. When the standard frequency deviation f/sub d/ are 5 Hz, 8 Hz. and 12 Hz, the SNR to meet the BER=10/sup -4/ in AWGN channel experiences the power penalty by about 0.6 dB, 1.0 dB and 1.7 dB in the QPSK scheme and about 1.9 dB, 3.2 dB and 67 dB in 16QAM modulation than the OFDM communication system without phase noise. Furthermore, the BER performance of the QPSK-OFDM communication system is considerably degraded because of the BER error floor if the phase noise standard frequency deviation f/sub d/ becomes greater than 30 Hz.

Removal of impulse noise from highly corrupted images by using noise position information and directional information of image

AbstractOne excellent method for restoration of images with superposed impulsive noise uses the position information of the impulsive noise for the pixels used for processing and of the processing point. This method consists of two steps. In Step 1, the impulsive noise existing in the image is detected and the noise position image is formed. In Step 2, by using the noise position image formed in Step 1, the filter processing is carried out on the pixels degraded by impulsive noise only with the pixels not affected by the impulsive noise. An excellent procedure for Step 2, using an average filter (PSA filter), has been proposed. However, in the method with an average filter, a uniform weight is provided on all pixels in the filter window. Therefore, if the generation probability of the impulsive noise is increased, the window size cannot be increased even if the filter window size should be increased. Also, an individual image has directionality specific to the image. This directionality is not taken into account in the filter processing. In the present paper, in order to resolve this problem, a PSWA filter is proposed for the filter processing in Step 2 by using the weighted average filter with weights considering the distance from the process point and the directionality of the image. In order to appropriately apply the proposed filter, there are two parameters (window size N and parameter κ) to be set. From experimental investigation, it is found that these two parameters do not depend on the type of the original image but only on the generation probability of the impulsive noise. Further, from the generation probability of the impulsive noise, the method for providing these two parameters is presented specifically. The effectiveness of the proposed method is confirmed through several processing examples. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 33–43, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1138