Gaussian noise

About: Gaussian noise is a research topic. Over the lifetime, 25934 publications have been published within this topic receiving 552078 citations.

An introduction to the theory of random signals and noise

Abstract: Preface to the IEEE Press Edition. Preface. Errata. Introduction. Probability. Random Variables and Probability Distributions. Averages. Sampling. Spectral Analysis. Shot Noise. The Gaussian Process. Linear Systems. Noise Figures. Optimum Linear Systems. Nonlinear Devices: The Direct Method. Nonlinear Devices: The Transform Method. Statistical Detection Signals. Appendix 1: The Impulse Function. Appendix 2: Integral Equations. Bibliography. Index.

Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$ -Constrained Quadratic Programming (Lasso)

Abstract: The problem of consistently estimating the sparsity pattern of a vector beta* isin Rp based on observations contaminated by noise arises in various contexts, including signal denoising, sparse approximation, compressed sensing, and model selection. We analyze the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering the sparsity pattern. Our main result is to establish precise conditions on the problem dimension p, the number k of nonzero elements in beta*, and the number of observations n that are necessary and sufficient for sparsity pattern recovery using the Lasso. We first analyze the case of observations made using deterministic design matrices and sub-Gaussian additive noise, and provide sufficient conditions for support recovery and linfin-error bounds, as well as results showing the necessity of incoherence and bounds on the minimum value. We then turn to the case of random designs, in which each row of the design is drawn from a N (0, Sigma) ensemble. For a broad class of Gaussian ensembles satisfying mutual incoherence conditions, we compute explicit values of thresholds 0 0, if n > 2 (thetasu + delta) klog (p- k), then the Lasso succeeds in recovering the sparsity pattern with probability converging to one for large problems, whereas for n < 2 (thetasl - delta)klog (p - k), then the probability of successful recovery converges to zero. For the special case of the uniform Gaussian ensemble (Sigma = Iptimesp), we show that thetasl = thetas

FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising

Abstract: Due to the fast inference and good performance, discriminative learning methods have been widely studied in image denoising. However, these methods mostly learn a specific model for each noise level, and require multiple models for denoising images with different noise levels. They also lack flexibility to deal with spatially variant noise, limiting their applications in practical denoising. To address these issues, we present a fast and flexible denoising convolutional neural network, namely FFDNet, with a tunable noise level map as the input. The proposed FFDNet works on downsampled sub-images, achieving a good trade-off between inference speed and denoising performance. In contrast to the existing discriminative denoisers, FFDNet enjoys several desirable properties, including: 1) the ability to handle a wide range of noise levels (i.e., [0, 75]) effectively with a single network; 2) the ability to remove spatially variant noise by specifying a non-uniform noise level map; and 3) faster speed than benchmark BM3D even on CPU without sacrificing denoising performance. Extensive experiments on synthetic and real noisy images are conducted to evaluate FFDNet in comparison with state-of-the-art denoisers. The results show that FFDNet is effective and efficient, making it highly attractive for practical denoising applications.

A scheme for robust distributed sensor fusion based on average consensus

Abstract: We consider a network of distributed sensors, where where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum-likelihood estimate of the parameters. This scheme doesn't involve explicit point-to-point message passing or routing; instead, it diffuses information across the network by updating each node's data with a weighted average of its neighbors' data (they maintain the same data structure). At each step, every node can compute a local weighted least-squares estimate, which converges to the global maximum-likelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected.

An Adaptive Detection Algorithm

Abstract: A general problem of signal detection in a background of unknown Gaussian noise is addressed, using the techniques of statistical hypothesis testing. Signal presence is sought in one data vector, and another independent set of signal-free data vectors is available which share the unknown covariance matrix of the noise in the former vector. A likelihood ratio decision rule is derived and its performance evaluated in both the noise-only and signal-plus-noise cases.