scispace - formally typeset
Search or ask a question
Topic

White noise

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


Papers
More filters
Journal ArticleDOI
01 Nov 1998
TL;DR: This paper shows how adaptive systems can learn to add an optimal amount of noise to some nonlinear feedback systems by derives the SR optimality conditions that any stochastic learning system should try to achieve.
Abstract: This paper shows how adaptive systems can learn to add an optimal amount of noise to some nonlinear feedback systems. This "stochastic resonance" (SR) effect occurs in a wide range of physical and biological systems. The noise energy can enhance the faint periodic signals or faint broadband signals that force the dynamical systems. Fuzzy and other adaptive systems can learn to induce SR based only on samples from the process. The paper derives the SR optimality conditions that any stochastic learning system should try to achieve. The adaptive system learns the SR effect as the system performs a stochastic gradient ascent on the signal-to-noise ratio. The stochastic learning scheme does not depend on a fuzzy system or any other adaptive system. Simulations test this SR learning scheme on the popular quartic-bistable dynamical system and on other dynamical systems. The driving noise types range from Gaussian white noise to impulsive noise to chaotic noise.

298 citations

01 Jan 2004
TL;DR: A general mathematical and experimental methodology to compare and classify classical image denoising algorithms is defined, and an algorithm (Non Local Means) addressing the preservation of structure in a digital image is proposed.
Abstract: The search for efficient image denoising methods still is a valid challenge, at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions, but fail in general and create artifacts or remove image fine structures. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms, second, to propose an algorithm (Non Local Means) addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise”, defined as the difference between a digital image and its denoised version. The NL-means algorithm is also proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods are compared in four ways ; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of L distances of the denoised version to the original image. The most powerful evaluation method seems, however, to be the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.

297 citations

Journal ArticleDOI
TL;DR: It is shown that an i.i.d. sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift f l/2 and variance 1/4n -l .
Abstract: Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam's deficiency distance $\Delta$ would make it precise. The models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. In nonparametrics, a first result of this kind has recently been established for Gaussian regression. We consider the analogous problem for the experiment given by n i.i.d. observations having density f on the unit interval. Our basic result concerns the parameter space of densities which are in a Holder ball with exponent $\alpha > 1/2$ and which are uniformly bounded away from zero. We show that an i. i. d. sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift $f^{1/2}$ and variance $1/4 n^{-1}$. This represents a nonparametric analog of Le Cam's heteroscedastic Gaussian approximation in the finite dimensional case. The proof utilizes empirical process techniques related to the Hungarian construction. White noise models on f and log f are also considered, allowing for various "automatic" asymptotic risk bounds in the i.i.d. model from white noise.

297 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derived minimum mean-square error estimators of speech DFT coefficient magnitudes as well as of complex-valued DFT coefficients based on two classes of generalized gamma distributions, under an additive Gaussian noise assumption.
Abstract: This paper considers techniques for single-channel speech enhancement based on the discrete Fourier transform (DFT). Specifically, we derive minimum mean-square error (MMSE) estimators of speech DFT coefficient magnitudes as well as of complex-valued DFT coefficients based on two classes of generalized gamma distributions, under an additive Gaussian noise assumption. The resulting generalized DFT magnitude estimator has as a special case the existing scheme based on a Rayleigh speech prior, while the complex DFT estimators generalize existing schemes based on Gaussian, Laplacian, and Gamma speech priors. Extensive simulation experiments with speech signals degraded by various additive noise sources verify that significant improvements are possible with the more recent estimators based on super-Gaussian priors. The increase in perceptual evaluation of speech quality (PESQ) over the noisy signals is about 0.5 points for street noise and about 1 point for white noise, nearly independent of input signal-to-noise ratio (SNR). The assumptions made for deriving the complex DFT estimators are less accurate than those for the magnitude estimators, leading to a higher maximum achievable speech quality with the magnitude estimators.

293 citations

Journal ArticleDOI
TL;DR: A comparison of PCA and ICA revealed significant differences in their treatment of both structured and random noise, while PCA was superior for isolation and removal of random noise.

292 citations


Network Information
Related Topics (5)
Nonlinear system
208.1K papers, 4M citations
83% related
Robustness (computer science)
94.7K papers, 1.6M citations
83% related
Estimator
97.3K papers, 2.6M citations
81% related
Communication channel
137.4K papers, 1.7M citations
80% related
Matrix (mathematics)
105.5K papers, 1.9M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537