Showing papers on "White noise published in 2006"
Book•
11 Jan 2006TL;DR: This book discusses Signal Processing Methods, Hidden Markov Models, Bayesian Estimation Theory, and Model-Based Power Spectral Estimation, which aims to improve the quality of signal processing in the rapidly changing environment.
Abstract: Contents Symbols Abbreviations 1 Introduction 1.1 Signals, Noise and Information 1.2 Signal Processing Methods 1.3 Applications of Digital Signal Processing 1.4 A Review of Sampling and Quantisation 1.5 Summary Bibliography 2 Noise and Distortion 2.1 Introduction 2.2 White Noise 2.3 Coloured Noise Pink Noise and Brown Noise 2.4 Impulsive and Click Noise 2.5 Impulsive and Click Noise 2.6 Thermal Noise 2.7 Shot Noise 2.8 Flicker (I/f) Noise 2.9 Burst Noise 2.10 Electromagnetic (Radio) Noise 2.11 Channel Distortions 2.12 Echo and Multi-path Reflections 2.13 Modelling Noise 2.14 Summary Bibliography 3 Information Theory and Probability Models 3.1 Introduction: Probability and Information Models 3.2 Random Processes 3.3 Probability Models 3.4 Information Models 3.5 Stationary and Non-stationary Processes 3.6 Expected Values of a Process 3.7 Some Useful Classes of Random Processes 3.8 Transformation of a Random Process 3.9 Search Engines: Citation Ranking 3.10 Summary Bibliography 4 Baseyian Inference 4.1 Bayesian Estimation Theory: Basic Definitions 4.2 Bayesian Estimation 4.3 The Estimate-Maximise Method 4.4 Cramer-Rao Bound on the Minimum Estimator Variance 4.5 Design of Gaussian Mixture Models 4.6 Bayesian Classification 4.7 Modeling the Space of a Random Process 4.8 Summary Bibliography 5 Hidden Markov Models 5.1 Statistical Models for Non-Stationary Processes 5.2 Hidden Markov Models 5.3 Training Hidden Markov Models 5.4 Decoding of Signals Using Hidden Markov Models 5.5 HMM In DNA and Protein Sequence Modelling 5.6 HMMs for Modelling Speech and Noise 5.7 Summary Bibliography 6 Least Square Error Wiener-Kolmogorov Filters 6.1 Least Square Error Estimation: Wiener-Kolmogorov Filter 6.2 Block-Data Formulation of the Wiener Filter 6.3 Interpretation of Wiener Filters as Projection in Vector Space 6.4 Analysis of the Least Mean Square Error Signal 6.5 Formulation of Wiener Filters in the Frequency Domain 6.6 Some Applications of Wiener Filters 6.7 Implementation of Wiener Filters 6.8 Summary Bibliography 7 Adaptive Filters, Kalman, RLS, LMS 7.1 Introduction 7.2 State-Space Kalman Filter 7.3 Extended Kalman Filter 7.4 Unscented Kalman Filter 7.5 Sample-Adaptive Filters 7.6 Recursive Least Square(RLS) Adaptive Filters 7.7 The Steepest-Descent Method 7.8 The LMS Filter 7.9 Summary Bibliography 8 Linear Prediction Models 8.1 Linear Prediction Coding 8.2 Forward, Backward and Lattice Predictors 8.3 Short-term and Long-Term Linear Predictors 8.4 MAP Estimation of Predictor Coefficients 8.5 Formant-Tracking LP Models 8.6 Sub-Band Linear Prediction 8.7 .i.Signal Restoration Using Linear Prediction Models 8.8 Summary Bibliography 9 Eigenvalue Analysis and Principal Component Analysis 9.1 Introduction 9.2 Eigen Analysis 9.3 Principal Component Analysis 9.4 Summary Bibliography 10 Power Spectrum Analysis 10.1 Power Spectrum and Correlation 10.2 Fourier Series: Representation of Periodic Signals 10.3.3 Energy-Spectral Density and Power-Spectral Density 10.3 Fourier Transform: Representation of Aperiodic Signals 10.4 Non-Parametric Power Spectrum Estimation 10.5 Model-Based Power Spectral Estimation 10.6 High Resolution Spectral Estimation Based on Subspace Eigen-Analysis 10.7 Summary Bibliography 11. Interpolation - Replacement of Lost Samples 11.1 Introduction 11.2 Model-Based Interpolation 11.3 Model-Based Interpolation 11.4 Summary Bibliography 12 Signal Enhancement via Spectral Amplitude Estimation 12.1Introduction 12.2 Spectral Representation of Noisy Signals 12.3 Vector Representation of Spectrum of Noisy Signals 12.4 Spectral Subtraction 12.5 Bayesian MMSE Spectral Amplitude Estimation 12.6 Estimation of Signal to Noise Ratios 12.7 Application to Speech Restoration and Recognition 12.8 Summary Bibliography 13 Impulsive Noise: Modelling, Detection and Removal 13.1 Impulsive Noise 13.2 Autocorrelation and Power Spectrum of Impulsive Noise 13.3 Probability Models for Impulsive Noise 13.4 Impulse contamination, Signal to Impulsive Noise Ratio 13.5 Median Filters 13.6 Impulsive Noise Removal Using Linear Prediction Models 13.7 Robust Parameter Estimation 13.8 Restoration of Archived Gramophone Records 13.9 Summary Bibliography 14 Transient Noise Pulses 14.1 Transient Noise Waveforms 14.2 Transient Noise Pulse Models 14.3 Detection of Noise Pulses 14.4 Removal of Noise Pulse Distortions 14.5 Summary Bibliography 15 Echo Cancellation 15.1 Introduction: Acoustic and Hybrid.i.Hybrid Echoes 15.2 Echo Return Time: The Sources of Delay in Communication Networks 15.3 Telephone Line Hybrid Echo 15.4 Hybrid Echo Suppression 15.5 .i.Adaptive Echo Cancellation 15.6 Acoustic .i.Echo 15.7 .i.Sub-band Acoustic Echo Cancellation 15.8 .i. Echo Cancellation with Linear Prediction Pre-whitening 15.9 Multiple-Input Multiple-Output (MIMO) Acoustic Echo Cancellation 15.10 Summary Bibliography 16 Channel Equalisation and Blind Deconvolution 16.1 Introduction 16.2 Blind-Deconvolution Using Channel Input Power Spectrum 16.3 Equalisation Based on Linear Prediction Models 16.4 Bayesian Blind Deconvolution and Equalisation 16.5 Blind Equalisation for Digital Communication Channels 16.6 Equalisation Based on Higher-Order Statistics 16.7 Summary 16.8 Bibliography 17 Speech Enhancement: Noise Reduction, Bandwidth Extension and Packet Replacement 17.1 An Overview of Speech Enhancement in Noise 17.2 Single-Input Speech Enhancement Methods 17.3 Speech Bandwidth Extension 17.4 Interpolation of Lost Speech Segments 17.5 Multiple-Input Speech Enhancement Methods 17.6 Speech Distortion Measurements 17.7 Summary 17.8 Bibliography 18 Multiple-Input Multiple-Output Systems, Independent Component Analysis 18.1 Introduction 18.2 MIMO Signal Propagation and Mixing Models 18.3 Independent Component Analysis 18.4 Summary Bibliography 19 Signal Processing in Mobile Communication 19.1 Introduction to Cellular Communication 19.2 Communication Signal Processing in Mobile Systems 19.3 Noise, Capacity and Spectral Efficiency 19.4 Multi-path and Fading in Mobile Communication 19.5 Smart Beam-forming Antennas 19.6 Summary Bibliography Index
1,000 citations
TL;DR: In this article, the authors developed a simple method to determine the effect of red noise on photometric planetary transit detections, and showed that the detection threshold in the presence of systematics can be much higher than that with the assumption of white noise and obeys a different dependence on magnitude, orbital period and the parameters of the survey.
Abstract: Since the discovery of short-period exoplanets a decade ago, photometric surveys have been recognized as a feasible method to detect transiting hot Jupiters. Many transit surveys are now underway, with instruments ranging from 10-cm cameras to the Hubble Space Telescope. However, the results of these surveys have been much below the expected capacity, estimated in the dozens of detections per year.
One of the reasons is the presence of systematics (‘red noise’) in photometric time-series. In general, yield predictions assume uncorrelated noise (‘white noise’). In this paper, we show that the effect of red noise on the detection threshold and the expected yields cannot be neglected in typical ground-based surveys. We develop a simple method to determine the effect of red noise on photometric planetary transit detections. This method can be applied to determine detection thresholds for transit surveys. We show that the detection threshold in the presence of systematics can be much higher than that with the assumption of white noise, and obeys a different dependence on magnitude, orbital period and the parameters of the survey. Our method can also be used to estimate the significance level of a planetary transit candidate (to select promising candidates for spectroscopic follow-up).
We apply our method to the OGLE planetary transit search, and show that it provides a reliable description of the actual detection threshold with real correlated noise. We point out in what way the presence of red noise could be at least partly responsible for the dearth of transiting planet detections from existing surveys, and examine some possible adaptations in survey planning and strategy. Finally, we estimate the photometric stability necessary to the detection of transiting ‘hot Neptunes’.
595 citations
TL;DR: A novel adaptive and patch-based approach is proposed for image denoising and representation based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel to associate with each pixel the weighted sum of data points within an adaptive neighborhood.
Abstract: A novel adaptive and patch-based approach is proposed for image denoising and representation. The method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel. Our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood, in a manner that it balances the accuracy of approximation and the stochastic error, at each spatial position. This method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point. By introducing spatial adaptivity, we extend the work earlier described by Buades et al. which can be considered as an extension of bilateral filtering to image patches. Finally, we propose a nearly parameter-free algorithm for image denoising. The method is applied to both artificially corrupted (white Gaussian noise) and real images and the performance is very close to, and in some cases even surpasses, that of the already published denoising methods
486 citations
TL;DR: This paper confirms that the spatial distribution of the various fMRI noise sources is similar to what has already been described in the literature and demonstrates, using diagnostic statistics, that removal of these contributions reduces first and higher order autocorrelation as well as non-normality in the residuals, thereby improving the validity of the drawn inferences.
442 citations
TL;DR: An analytically exact method is proposed to extract the signal intensity and the noise variance simultaneously from noisy magnitude MR signals using a fixed point formula of signal-to-noise ratio (SNR) and a correction factor.
304 citations
TL;DR: A large class of valid models that incorporate flow and stream distance by using spatial moving averages are developed by running the moving average function upstream from a location, and by construction they are valid models based on stream distance.
Abstract: We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.
276 citations
TL;DR: In this article, the existence of a compact global random attractor within the set of tempered random bounded sets was shown to converge under the forward flow to a random compact invariant set.
Abstract: We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term and additive independent white noise at each node. We prove the existence of a compact global random attractor within the set of tempered random bounded sets. An interesting feature of this is that, even though the spatial domain is unbounded and the solution operator is not smoothing or compact, pulled back bounded sets of initial data converge under the forward flow to a random compact invariant set.
275 citations
TL;DR: The analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by Lévy stable noises recovers in this limit the standard results for the Fokker-Planck dynamics driven by Gaussian white noise.
Abstract: We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by Levy stable noises. The complexity of the first passage time statistics (mean first passage time, cumulative first passage time distribution) is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non-Gaussian noises. The validity of the method is tested numerically and compared against analytical formulas when the stability index alpha approaches 2, recovering in this limit the standard results for the Fokker-Planck dynamics driven by Gaussian white noise.
128 citations
TL;DR: Low-pass filtering the ADC subchannels to this alias-free band reduces the blind calibration problem to a conventional gain and time delay estimation problem for an unknown signal in noise.
Abstract: In this paper, we describe a blind calibration method for gain and timing mismatches in a two-channel time-interleaved low-pass analog-to-digital converters (ADC). The method requires that the input signal should be slightly oversampled. This ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the ADC subchannels are alias free. Low-pass filtering the ADC subchannels to this alias-free band reduces the blind calibration problem to a conventional gain and time delay estimation problem for an unknown signal in noise. An adaptive filtering structure with three fixed FIR filters and two adaptive gain and delay parameters is employed to achieve the calibration. A convergence analysis is presented for the blind calibration technique. Numerical simulations for a bandlimited white noise input and for inputs containing several sinusoidal components demonstrate the effectiveness of the proposed method
123 citations
TL;DR: In particular, it has escaped attention until recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime as discussed by the authors.
Abstract: Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications — the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.
112 citations
TL;DR: A finite-horizon robust Kalman filtering approach for discrete time-varying uncertain systems with additive uncertain-covariance white noises with minimal upper bound on the state estimation error covariance for all admissible uncertainties is presented.
Abstract: A finite-horizon robust Kalman filtering approach for discrete time-varying uncertain systems with additive uncertain-covariance white noises is presented. The system under consideration is subject to uncertainties in both the state and output matrices. The state and gain matrices of the filter are optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties
TL;DR: In particular, it has escaped attention until recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime as mentioned in this paper.
Abstract: Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {\em analytically-solvable} situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications -- the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on a par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.
TL;DR: It is argued that ASL data are best viewed in the same data analytic framework as BOLD fMRI data, in that all scans are modeled and colored noise is accommodated.
TL;DR: The results show that the technique is more suitable for processing heavy noised ultrasonic signals, and it can also be used in automatic flaw detection.
TL;DR: In this article, a generalization of the Heston model is proposed, which consists of two coupled stochastic differential equations, one for the stock price and the other for the volatility.
Abstract: We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.
TL;DR: The proposed approach, which utilizes the first-order as well as higher order linear prediction terms simultaneously but does not require phase unwrapping, can be considered as a generalized version of the weighted linear predictor frequency estimator.
Abstract: Based on linear prediction and weighted least squares, three simple iterative algorithms for frequency estimation of a complex sinusoid in additive white noise are devised. The proposed approach, which utilizes the first-order as well as higher order linear prediction terms simultaneously but does not require phase unwrapping, can be considered as a generalized version of the weighted linear predictor frequency estimator. In particular, convergence as well as mean and variance analysis of the most computationally efficient frequency estimator, namely, GWLP 2, are provided. Computer simulations are included to contrast the performance of the proposed algorithms with several conventional computationally attractive frequency estimators and Crame/spl acute/r-Rao lower bound for different frequencies, observation lengths, and signal-to-noise ratios.
TL;DR: It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling and supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators.
Abstract: In the paper, complete synchronization of two chaotic oscillators via unidirectional coupling determined by white noise distribution is investigated. It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling. The established theoretical result supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators. Furthermore, numerical examples are provided to illustrate some possible applications of the theoretical result.
TL;DR: In this paper, the authors analysed 12 years of DORIS data from 31 selected sites of the IGN/JPL (Institut Geographique National/Jet Propulsion Laboratory) solution IGNWD05 in an attempt to understand the nature of the noise in the weekly station coordinate time series.
Abstract: Twelve years of DORIS data from 31 selected sites of the IGN/JPL (Institut Geographique National/Jet Propulsion Laboratory) solution IGNWD05 have been analysed using maximum likelihood estimation (MLE) in an attempt to understand the nature of the noise in the weekly station coordinate time-series. Six alternative noise models in a total of 12 different combinations were used as possible descriptions of the noise. The six noise models can be divided into two natural groups, temporally uncorrelated (white) noise and temporally correlated (coloured) noise. The noise can be described as a combination of variable white noise and one of flicker, first-order Gauss–Markov or power-law noise. The data set as a whole is best described as a combination of variable white noise plus flicker noise. The variable white noise, which is white noise with variable amplitude that is a function of the weekly formal errors multiplied by an estimated scale factor, shows a dependence on site latitude and the number of DORIS-equipped satellites used in the solution. The latitude dependence is largest in the east component due to the near polar orbit of the SPOT satellites. The amplitude of the flicker noise is similar in all three components and equal to about 20 mm/year1/4. There appears to be no latitude dependence of the flicker noise amplitude. The uncertainty in rates (site velocities) after 12 years is just under 1 mm/year. These uncertainties are around 3–4 times larger than if only variable white noise had been assumed, i.e., no temporally correlated noise. A rate uncertainty of 1 mm/year after 12 years in the vertical is similar to that achieved using Global Positioning System (GPS) data but it takes DORIS twice as long to reach 1 mm/year than GPS in the horizontal. The analysis has also helped to identify sites with either anomalous noise characteristics or large noise amplitudes, and tested the validity of previously proposed discontinuities. In addition, several new offsets were found in the time-series that should be used or at least flagged in future work.
Posted Content•
TL;DR: It is shown that nonparametric regression is asymptotically equivalent, in Le Cam's sense, to a sequence of Gaussian white noise experiments as the number of observations tends to infinity.
Abstract: We show that nonparametric regression is asymptotically equivalent in Le Cam's sense with a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework based on approximation spaces, which permits to achieve asymptotic equivalence even in the cases of multivariate and random design.
TL;DR: In this paper, the Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems.
TL;DR: In this article, the dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied, where a correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamic of the two species.
Abstract: The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.
TL;DR: In this paper, an adaptation of the standard Grassberger-Proccacia (GP) algorithm for estimating the correlation dimension of a time series in a non-subjective manner is presented.
TL;DR: The proposed distributed stochastic power control scheme minimize the sum of variances of mobile's transmission power and signal-to-interference error and works fine with 4-bit quantization.
Abstract: In this paper, the uplink power control problem is considered for CDMA cellular systems, where stochastic SIR measurements are performed at base stations. A distributed stochastic power control algorithm is proposed assuming SIR measurements contain white noise. The proposed scheme minimize the sum of variances of mobile's transmission power and signal-to-interference error. The algorithm derived is fully distributed in the sense that each user only needs to know its own signal-to-interference measurement and channel variation. Uncertainties of wireless channels are accommodated by using a robust estimator. Simulation results indicate that the proposed power control scheme has very fast convergence. In addition, it also works fine with 4-bit quantization.
TL;DR: Experiments on a single-walled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finite-variance and infinite-Variance noise: small amounts of noise enhanced the nanotubes detector's performance.
Abstract: Electrical noise can help pulse-train signal detection at the nanolevel. Experiments on a single-walled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finite-variance and infinite-variance noise: small amounts of noise enhanced the nanotube detector's performance. The experiments used a carbon nanotube field-effect transistor to detect noisy subthreshold electrical signals. Two new SR hypothesis tests in the Appendix also confirmed the SR effect in the nanotube transistor. Three measures of detector performance showed the SR effect: Shannon's mutual information, the normalized correlation measure, and an inverted bit error rate compared the input and output discrete-time random sequences. The nanotube detector had a threshold-like input-output characteristic in its gate effect. It produced little current for subthreshold digital input voltages that fed the transistor's gate. Three types of synchronized white noise corrupted the subthreshold Bernoulli sequences that fed the detector. The Gaussian, the uniform, and the impulsive Cauchy noise combined with the random input voltage sequences to help the detector produce random output current sequences. The experiments observed the SR effect by measuring how well an output sequence matched its input sequence. Shannon's mutual information used histograms to estimate the probability densities and computed the entropies. The correlation measure was a scalar inner product of the input and output sequences. The inverted bit error rate computed how often the bits matched between the input and output sequences. The observed nanotube SR effect was robust: it persisted even when infinite-variance Cauchy noise corrupted the signal stream. Such noise-enhanced signal processing at the nanolevel promises applications to signal detection in wideband communication systems and biological and artificial neural networks
TL;DR: A number of IS data approaches that parallel the methods most commonly used for spectral analysis of RS data: the periodogram (PER), the Capon method (CAP), the multiple-signal characterization method (MUSIC), and the estimation of signal parameters via rotational invariance technique (ESPRIT).
TL;DR: This work considers the detection of an unknown and arbitrary rank-one signal in a spatial sector scanned by a small number m of beams and derives the generalized-likelihood ratio test (GLRT) along with expressions for its probability density function under both hypotheses.
Abstract: We consider the detection of an unknown and arbitrary rank-one signal in a spatial sector scanned by a small number m of beams. We address the problem of finding the maximal invariant for the problem at hand and show that it consists of the ratio of the eigenvalues of a Wishart matrix to its trace. Next, we derive the generalized-likelihood ratio test (GLRT) along with expressions for its probability density function (pdf) under both hypotheses. Special attention is paid to the case m=2, where the GLRT is shown to be a uniformly most powerful invariant (UMPI). Numerical simulations attest to the validity of the theoretical analysis and illustrate the detection performance of the GLRT
TL;DR: A theory is constructed that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations and a random noninvertible one-dimensional map.
Abstract: We demonstrate, within the framework of the FitzHugh-Nagumo model, that a firing neuron can respond to a noisy driving in a nonreliable manner: the same Gaussian white noise acting on identical neurons evokes different patterns of spikes. The effect is characterized via calculations of the Lyapunov exponent and the event synchronization correlations. We construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations. Geometrically, the antireliability is described by a random noninvertible one-dimensional map.
TL;DR: This study focuses on regenerating the time domain model of roads by using a white noise filtration method, especially on the temporally and spatially correlative bilateral track model by taking the coherence between the road tracks into consideration.
TL;DR: The results demonstrate that the best achievable rates of convergence are determined both by smooths of the function away from the change-point and by the degree of ill-posedness of the convolution operator.
Abstract: We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of convergence are determined both by smoothness of the function away from the change-point and by the degree of ill-posedness of the convolution operator. Optimality is obtained by introducing a new technique that involves, as a key element, detection of zero crossings of an estimate of the properly smoothed second derivative of the underlying function.
TL;DR: A noise model is proposed that better fits the images captured from typical imaging devices and a simple method to extract necessary parameters directly from the images without any prior knowledge of imaging pipeline algorithms implemented in the imaging devices is described.
Abstract: Many conventional image processing algorithms such as noise filtering, sharpening and deblurring, assume a noise model of Additive White Gaussian Noise (AWGN) with constant standard deviation throughout the image. However, this noise model does not hold for images captured from typical imaging devices such as digital cameras, scanners and camera-phones. The raw data from the image sensor goes through several image processing steps such as demosaicing, color correction, gamma correction and JPEG compression, and thus, the noise characteristics in the final JPEG image deviates significantly from the widely-used AWGN noise model. Thus, when the image processing algorithms are applied to the digital photographs, they may not provide optimal image quality after the image processing due to the inaccurate noise model. In this paper, we propose a noise model that better fits the images captured from typical imaging devices and describe a simple method to extract necessary parameters directly from the images without any prior knowledge of imaging pipeline algorithms implemented in the imaging devices. We show experimental results of the noise parameters extracted from the raw and processed digital images.