Distribution Of Additive Noise Research Articles

Baseline correction for Raman spectra using a spectral estimation-based asymmetrically reweighted penalized least squares method.

Baseline correction is necessary for the qualitative and quantitative analysis of samples because of the existence of background fluorescence interference in Raman spectra. The asymmetric least squares (ALS) method is an adaptive and automated algorithm that avoids peak detection operations along with other user interactions. However, current ALS-based improved algorithms only consider the smoothness configuration of regions where the signals are greater than the fitted baseline, which results in smoothing distortion. In this paper, an asymmetrically reweighted penalized least squares method based on spectral estimation (SEALS) is proposed. SEALS considers not only the uniform distribution of additive noise along the baseline but also the energy distribution of the signal above and below the fitted baseline. The energy distribution is estimated using inverse Fourier and autoregressive models to create a spectral estimation kernel. This kernel effectively optimizes and balances the asymmetric weight assigned to each data point. By doing so, it resolves the issue of local oversmoothing that is typically encountered in the asymmetrically reweighted penalized least squares method. This oversmoothing problem can negatively impact the iteration depth and accuracy of baseline fitting. In comparative experiments on simulated spectra, SEALS demonstrated a better baseline fitting performance compared to several other advanced baseline correction methods, both under moderate and strong fluorescence backgrounds. It has also been proven to be highly resistant to noise interference. When applied to real Raman spectra, the algorithm correctly restored the weak peaks and removed the fluorescence peaks, demonstrating the effectiveness of this method. The computation time of the proposed method was approximately 0.05s, which satisfies the real-time baseline correction requirements of practical spectroscopy acquisition.

Special aspects of using a new non-stationary random processes analysis approach in the conditions of a priori uncertainty of the useful signal function

The paper considers the use of a new method of signal processing in the time domain under conditions of a limited amount of a priori information about the useful signal function and the statistical characteristics of additive noise. Research have shown its high efficiency in processing signals both local and global, using it to detect anomalous measurements, eliminating the systematic component in the case of a onesided law of the distribution of additive noise and a number of others.

Switching criterion for sub-and super-Gaussian additive noise in adaptive filtering

Abstract Additive noise distributions can be divided into three types: Gaussian, super- and sub-Gaussian. The existing algorithms for adaptive filtering do not provide a better performance than the least mean square (LMS) method for the super- and sub-Gaussian noise simultaneously. For example, the maximum correntropy criterion performs better (worse) than the LMS method for super-Gaussian (sub-Gaussian) noise, whereas the least mean fourth performs better (worse) than the LMS method for sub-Gaussian (super-Gaussian) noise. We propose a criterion for switching between sub- and super- Gaussian additive noise, that could be used to assess whether the error signal had a sub- or super-Gaussian profile, and thus determine which algorithm would work best in the iterative process. Simulations demonstrate that the switching criterion helps the proposed switching algorithm to produce a better performance than the LMS algorithm for sub and super-Gaussian noise simultaneously.

Predictability of fat-tailed extremes.

We conjecture for a linear stochastic differential equation that the predictability of threshold exceedances (I) improves with the event magnitude when the noise is a so-called correlated additive-multiplicative noise, no matter the nature of the stochastic innovations, and also improves when (II) the noise is purely additive, obeying a distribution that decays fast, i.e., not by a power law, and (III) deteriorates only when the additive noise distribution follows a power law. The predictability is measured by a summary index of the receiver operating characteristic curve. We provide support to our conjecture-to compliment reports in the existing literature on (II)-by a set of case studies. Calculations for the prediction skill are conducted in some cases by a direct numerical time-series-data-driven approach and in other cases by an analytical or semianalytical approach developed here.

Maximum likelihood optimal and robust Support Vector Regression with lncosh loss function

In this paper, a novel and continuously differentiable convex loss function based on natural logarithm of hyperbolic cosine function, namely lncosh loss, is introduced to obtain Support Vector Regression (SVR) models which are optimal in the maximum likelihood sense for the hyper-secant error distributions. Most of the current regression models assume that the distribution of error is Gaussian, which corresponds to the squared loss function and has helpful analytical properties such as easy computation and analysis. However, in many real world applications, most observations are subject to unknown noise distributions, so the Gaussian distribution may not be a useful choice. The developed SVR model with the parameterized lncosh loss provides a possibility of learning a loss function leading to a regression model which is maximum likelihood optimal for a specific input–output data. The SVR models obtained with different parameter choices of lncosh loss with ε-insensitiveness feature, possess most of the desirable characteristics of well-known loss functions such as Vapnik’s loss, the Squared loss, and Huber’s loss function as special cases. In other words, it is observed in the extensive simulations that the mentioned lncosh loss function is entirely controlled by a single adjustable λ parameter and as a result, it allows switching between different losses depending on the choice of λ. The effectiveness and feasibility of lncosh loss function are validated through a number of synthetic and real world benchmark data sets for various types of additive noise distributions.

Noise enhanced hypothesis-testing according to restricted Neyman–Pearson criterion

Noise enhanced hypothesis-testing is studied according to the restricted Neyman–Pearson (NP) criterion. First, a problem formulation is presented for obtaining the optimal probability distribution of additive noise in the restricted NP framework. Then, sufficient conditions for improvability and nonimprovability are derived in order to specify if additive noise can or cannot improve detection performance over scenarios in which no additive noise is employed. Also, for the special case of a finite number of possible parameter values under each hypothesis, it is shown that the optimal additive noise can be represented by a discrete random variable with a certain number of point masses. In addition, particular improvability conditions are derived for that special case. Finally, theoretical results are provided for a numerical example and improvements via additive noise are illustrated.

Average Bit Error Probability of Binary Coherent Signaling over Generalized Fading Channels Subject to Additive Generalized Gaussian Noise

This letter considers the average bit error probability of binary coherent signaling over flat fading channels subject to additive generalized Gaussian noise. More specifically, a generic closed form expression in terms of the Fox's H function is offered for the extended generalized-K fading case. Simplifications for some special fading distributions such as generalized-K fading and Nakagami-m fading and special additive noise distributions such as Gaussian and Laplacian noise are then presented. Finally, the mathematical formalism is illustrated by some numerical examples verified by computer based simulations for a variety of fading and additive noise parameters.

Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework

Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M -ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results.

Noise Enhanced Nonparametric Detection

This paper investigates potential improvement of nonparametric detection performance via addition of noise and evaluates the performance of noise modified nonparametric detectors. Detection performance comparisons are made between the original detectors and noise modified detectors. Conditions for improvability as well as the optimum additive noise distributions of the widely used sign detector, the Wilcoxon detector, and the dead-zone limiter detector are derived. Finally, a simple and fast learning algorithm to find the optimal noise distribution solely based on received data is presented. A near-optimal solution can be found quickly based on a relatively small dataset.

Too Much Mobility Limits the Capacity of Wireless Ad Hoc Networks

We show that for highly mobile ad hoc networks, the benefits of mobility are overshadowed by the cost of mobility in terms of the increased channel uncertainty and network homogeneity. We assume a block-fading channel model with jointly isotropic fading. We allow relays which can transmit and receive simultaneously. Under fairly general assumptions for the users' channel fades and additive noise distributions we show that increasing the number of transmit antennas M at any node beyond the channel coherence time T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (measured in units of channel uses) does not affect the capacity region of the ad hoc network. For a fast-fading (coherence time T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> lesM) homogeneous network, we determine the exact capacity region of the ad hoc network for any partition of the nodes into source, destination, and relay nodes. The optimal strategy is such that only one pair of source-destination nodes is active at a time while all the other nodes are inactive. There is no benefit from relaying and at high signal-to-noise ratio (SNR) the total throughput grows at most double-logarithmically with the number of nodes. Even for the case of slow fading, where the channel variations are slow enough that the receiver can track the channel perfectly, the inability of the transmitter to track the network topology limits the total throughput growth rate to no more than logarithmic in the number of nodes. Spatial correlation is shown to enhance the capacity region of the Rayleigh-fading ad hoc network

Toward improved ranking metrics

In many computer vision algorithms, a metric or similarity measure is used to determine the distance between two features. The Euclidean or SSD (sum of the squared differences) metric is prevalent and justified from a maximum likelihood perspective when the additive noise distribution is Gaussian. Based on real noise distributions measured from international test sets, we have found that the Gaussian noise distribution assumption is often invalid. This implies that other metrics, which have distributions closer to the real noise distribution, should be used. In this paper, we consider three different applications: content-based retrieval in image databases, stereo matching, and motion tracking. In each of them, we experiment with different modeling functions for the noise distribution and compute the accuracy of the methods using the corresponding distance measures. In our experiments, we compared the SSD metric, the SAD (sum of the absolute differences) metric, the Cauchy metric, and the Kullback relative information. For several algorithms from the research literature which used the SSD or SAD, we showed that greater accuracy could be obtained by using the Cauchy metric instead.

Optical processing of speckle images with bacteriorhodopsin for pattern recognition

Logarithmic processing of images with multiplicative noise characteristics can be utilized to transform an image into one with an additive noise distribution. This simplifies subsequent image processing steps for applications such as image restoration or correlation for pattern recognition. One particularly common form of multiplicative noise is speckle, for which the logarithmic operation not only produces additive noise, but also makes it of constant variance (signal-independent). I examine the optical transmission properties of some bacteriorhodopsin films here and find them well suited to implement such a pointwise logarithmic transformation optically in a parallel fashion. I present experimental results of the optical conversion of speckle images into transformed images with additive, signal-independent noise statistics using the real-time photochromic properties of bacteriorhodopsin. I provide an example of improved correlation performance in terms of correlation peak signal-to-noise for such a transformed speckle image.

Asymptotically robust detection for known signals in contaminated multiplicative noise

Abstract Robust detection of known weak signals of unknown amplitude is considered for a class of combined additive and nonadditive noise models and an asymptotically large set of independent observations. Cases where the additive noise distribution is known only to be a member of the Tukey-Huber contamination class of symmetric distributions and cases where the observation model is also known only to be a member of a particular class of multiplicative noise models are considered. The finite-sample-size performance of our schemes is found to be relatively insensitive to variations in the additive noise distribution and the observation model in a specific example.

Asymptotically robust detection of known signals in nonadditive noise

Robust detection of known weak signals of unknown amplitude is considered for a class of combined additive and nonadditive noise models and an asymptotically large set of independent observations. This class includes observation models that may have combinations of multiplicative and signal-dependent noise terms. Sufficient conditions are given for robust detection schemes for cases where the general form of the observation model is known but the additive noise distribution is known only to be a member of a general convex uncertainty class. Robust schemes satisfying these conditions are found for some example cases where additive signals and noise have been processed by memoryless nonlinearities. Some interesting example cases of combined multiplicative and signal-dependent noise are shown to use redescending nonlinearities, instead of the limiter nonlinearities typically found for similar additive noise cases. >

Parametric and nonparametric detectors based on a sequential sample median test

In the first part of this paper a sequential detection procedure, based on a Sequential Sample Median Test (S.S.M.T.), is introduced for the problem of discriminating between shift alternatives (constant signals in additive noise), in a specified noise environment. This detection procedure is shown to have the desirable properties of ease of implementation and of comparing favorably with efficient rank vector detection procedures. The decision samples are acquired in data groups of M samples on which an intermediate decision, based on the value of the sample median of the data group, is made. The final decision to accept one of the two hypotheses is based on the sum of the intermediate decisions. Each intermediate decision is made by comparing the sample median to two decision thresholds. These thresholds are determined by (i) having the probability of error and average sample size under the two hypotheses equal and (ii) specifying either the average sample size or average probability of error. For both types of constraints a numerical optimization procedure to find the “optimum≓ value of M is used. Specific results are obtained for additive gaussian and Cauchy noise. However, to apply this test to either problem it is necessary to know the c.d.f. of the decision samples, i.e., the decision thresholds are a function of the additive noise distribution, and this c.d.f. may not be known. In the second part of this paper an extension of the S.S.M.T. to an unspecified noise environment, for the average sample size constraint, is presented. Two recursive procedures are developed for estimating the decision thresholds corresponding to the desired average sample size. Both procedures are based on the Robbins-Monro stochastic approximation concept and are shown to converge with probability 1 to the correct decision threshold.