White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

ECG Denoising Using Marginalized Particle Extended Kalman Filter With an Automatic Particle Weighting Strategy

Abstract: In this paper, a model-based Bayesian filtering framework called the “marginalized particle-extended Kalman filter (MP-EKF) algorithm” is proposed for electrocardiogram (ECG) denoising. This algorithm does not have the extended Kalman filter (EKF) shortcoming in handling non-Gaussian nonstationary situations because of its nonlinear framework. In addition, it has less computational complexity compared with particle filter. This filter improves ECG denoising performance by implementing marginalized particle filter framework while reducing its computational complexity using EKF framework. An automatic particle weighting strategy is also proposed here that controls the reliance of our framework to the acquired measurements. We evaluated the proposed filter on several normal ECGs selected from MIT-BIH normal sinus rhythm database. To do so, artificial white Gaussian and colored noises as well as nonstationary real muscle artifact (MA) noise over a range of low SNRs from 10 to −5 dB were added to these normal ECG segments. The benchmark methods were the EKF and extended Kalman smoother (EKS) algorithms which are the first model-based Bayesian algorithms introduced in the field of ECG denoising. From SNR viewpoint, the experiments showed that in the presence of Gaussian white noise, the proposed framework outperforms the EKF and EKS algorithms in lower input SNRs where the measurements and state model are not reliable. Owing to its nonlinear framework and particle weighting strategy, the proposed algorithm attained better results at all input SNRs in non-Gaussian nonstationary situations (such as presence of pink noise, brown noise, and real MA). In addition, the impact of the proposed filtering method on the distortion of diagnostic features of the ECG was investigated and compared with EKF/EKS methods using an ECG diagnostic distortion measure called the “Multi-Scale Entropy Based Weighted Distortion Measure” or MSEWPRD. The results revealed that our proposed algorithm had the lowest MSEPWRD for all noise types at low input SNRs. Therefore, the morphology and diagnostic information of ECG signals were much better conserved compared with EKF/EKS frameworks, especially in non-Gaussian nonstationary situations.

Maximum likelihood estimation of the parameters of discrete fractionally differenced Gaussian noise process

Abstract: A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N/sup 2//2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise. >

Green-noise digital halftoning

Abstract: In this paper, we introduce the concept of green noise-the multifrequency component of white noise-and its advantages over blue noise for digital halftoning. Unlike blue-noise dither patterns, which are composed exclusively of isolated pixels, green-noise dither patterns are composed of pixel-clusters making them less susceptible to image degradation from nonideal printing artifacts such as dot-gain. Although they are not the only techniques which generate clustered halftones, error-diffusion with output-dependent feedback and variations based on filter weight perturbation are shown to be good generators of green noise, thereby allowing for tunable coarseness. Using statistics developed for blue noise, we closely examine the spectral content of resulting dither patterns. We introduce two spatial-domain statistics for analyzing the spatial arrangement of pixels in aperiodic dither patterns, because green noise patterns may be anisotropic, and therefore spectral statistics based on radial averages may be inappropriate for the study of these patterns.

On rates of convergence of efficient detection criteria in signal processing with white noise

Abstract: L.C. Zhao et al. (1986) proposed certain information-theoretic criteria for detection of the number of signals under an additive model with white noise when the noise variance is known or unknown. It was shown that these criteria are strongly consistent even when the underlying distribution is not necessarily Gaussian. Upper bounds on the probabilities of error detection are obtained here. >