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White noise

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


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TL;DR: A necessary and sufficient condition is given to model the output of a quantizer as an infinite-precision input and an additive, uniform, white noise.
Abstract: In this paper, a necessary and sufficient condition is given to model the output of a quantizer as an infinite-precision input and an additive, uniform, white noise. The statistical properties of the quantization error are studied, and a detailed analysis for Gaussian distributed inputs is given.

492 citations

Journal ArticleDOI
TL;DR: The authors model a finite-dimensional system as an ARMA (autoregressive moving-average) rational function of known orders, but the special cases of AR, MA, and all-pass models are also considered.
Abstract: A method is presented for identification of linear, time-variant, nonminimum phase systems when only output data are available. The input sequence need not be independent, but it must be non-Gaussian, with some special properties described in the test. The authors model a finite-dimensional system as an ARMA (autoregressive moving-average) rational function of known orders, but the special cases of AR, MA, and all-pass models are also considered. To estimate the parameters of their model, the authors utilize both second- and higher-order statistics of the output, which may be contaminated by additive, zero-mean, Gaussian white noise of unknown variance. The parameter estimators obtained are proved, under mild conditions, to be consistent. Simulations verify the performance of the proposed method in the case of relatively low signal-to-noise ratios, and when there is a model-order mismatch. >

492 citations

Journal ArticleDOI
TL;DR: An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated, using a mixture of an atom of probability at zero and a heavy-tailed density y with the mixing weight chosen by marginal maximum likelihood.
Abstract: An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density y, with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences. If estimation is then carried out using the posterior median, this is a random thresholding procedure. Other thresholding rules employing the same threshold can also be used. Probability bounds on the threshold chosen by the marginal maximum likelihood approach lead to overall risk bounds over classes of signal sequences of length n, allowing for sparsity of various kinds and degrees. The signal classes considered are nearly black sequences where only a proportion η is allowed to be nonzero, and sequences with normalized p norm bounded by η, for η > 0 and 0 1. Simulations show excellent performance. For appropriately chosen functions y, the method is computationally tractable and software is available. The extension to a modified thresholding method relevant to the estimation of very sparse sequences is also considered.

489 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this article, the seafloor is modeled as a stationary, zero-mean, Gaussian random field completely specified by its two-point covariance function, and the second moments are used as data functionals.
Abstract: At scale lengths less than 100 km or so, statistical descriptions of seafloor morphology can be usefully employed to characterize ridge crest processes, off-ridge tectonics and vulcanism, sedimentation, and postdepositional transport. We seek to develop methods for the estimation of seafloor statistics that take into account the finite precision, resolution, and sampling obtained by actual echo sounding systems. In this initial paper we restrict our attention to the problem of recovering second-order statistics from data sets collected by multibeam devices such as Sea Beam. The seafloor is modeled as a stationary, zero-mean, Gaussian random field completely specified by its two-point covariance function. We introduce an anisotropic two-point covariance function that has five free parameters describing the amplitude, orientation, characteristic wave numbers, and Hausdorff (fractal) dimension of seafloor topography. We formulate the general forward problem relating this model to the statistics of an ideal multibeam echo sounder, in particular the along-track autocovariance functions of individual beams and the cross-covariance functions between beams of arbitrary separation. Using these second moments as data functionals, we then pose the inverse problem of estimating the seafloor parameters from realistic, noisy data sets with finite sampling and beamwidth, and we solve this inverse problem by an iterative, linearized, least squares method. The inversion method is applied to Sea Beam transit data from both the Pacific and Atlantic oceans. Sea Beam system noise stands out as a sharp spike on the along-track autocovariance function and can be modeled as a white noise process whose amplitude generally increases with beam angle. The five parameters in our second-order model can be estimated from the inversion of data sets comprising ∼100–200 km of track length. In general, the cross-track wave number is the most poorly determined, although uncertainties in the assumed Sea Beam response may bias the values of the fractal dimension. Using the assumed beamwidth, the measured noise values, and the seafloor parameters recovered from the inversion, we generate Sea Beam “synthetics” whose statistical character can be directly compared with raw Sea Beam data. For most of the track segments we have processed thus far the synthetics are similar to the data. In the case of one Atlantic profile, however, the comparison clearly indicates the necessity of incorporating higher-order statistics. The space domain procedures described in this paper can be extended for this purpose.

481 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537