Gaussian noise

Summary

In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed. The probability density function p of a Gaussian random variable z is given by: : \varphi(z) = \frac 1 {\sigma\sqrt{2\pi}} e^{ -(z-\mu)^2/(2\sigma^2) } where z represents the grey level, \mu the mean grey value and \sigma its standard deviation. A special case is white Gaussian noise, in which the values at any pair of times are identically distributed and statistically independent (and hence uncorrelated). In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white

Official source

https://en.wikipedia.org/wiki/Gaussian_noise

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We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we establish strong local nondeterminism of the solution and the existence of jointly continuous local times. We also study the differentiability and moduli of continuity of the local times and deduce some sample path properties of the solution.

SPRINGER BIRKHAUSER2022

Random codes based on quasigroups (RCBQ) are cryptcodes, i.e. they are error-correcting codes, which provide information security. Cut-Decoding and 4-Sets-Cut-Decoding algorithms for these codes are defined elsewhere. Also, the performance of these codes for the transmission of text messages is investigated elsewhere. In this study, the authors investigate the RCBQ's performance with Cut-Decoding and 4-Sets-Cut-Decoding algorithms for transmission of images and audio files through a Gaussian channel. They compare experimental results for both coding/decoding algorithms and for different values of signal-to-noise ratio. In all experiments, the differences between the transmitted and decoded image or audio file are considered. Experimentally obtained values for bit-error rate and packet error rate and the decoding speed of both algorithms are compared. Also, two filters for enhancing the quality of the images decoded using RCBQ are proposed.

2019

Simulation of 1D ARPES Data and Measures to recover the underlying Signal

Nadine Gächter

Fourier deconvolution is a good tool to remove the blurring of images with a very high SNR. However it suffers under severe noise degradation and becomes impracticable at a SNR of 20dB. If the convolution width is very high this happens even earlier. The analysis of the frequency spectrum brings information on the data, especially on the periodicity of certain features. Furthermore it can be used to better understand other processing tools. Gaussian blur and smoothing can be used with the goal to enhance image structures at different scales. They have the effect of reducing high frequency information, corresponding to high pixel to pixel variation and usually a characteristic of noise. However it also reduces detail. In 2D better resultsmay be obtained, because diagonal pixels can be used in addition. Gaussian smoothing is certainly a useful tool in the analysis of ARPES data and it should be well integrated in other measures of data recovery. If the blurring of the signal is high it is beneficial apply some Gaussian blur before proceeding to other measures. If the blurring of the signal is low, it is better to apply Gaussian smoothing only after de-convolution measures in order to not loose information on the signal.