Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
Citations
More filters
15 Jun 2020
TL;DR: The data-driven Bayesian image analysis in Fourier space (DD-BIFS) modeling approach is described, illustrated it’s computational efficiency and speed, and given specific applications to improve the quality of arterial-spin-labeling images via a database of human brain positron emission tomography images.
Abstract: Statistical image analysis is an extensive field that includes problems such as noise-reduction, de-blurring, feature enhancement, and object detection/identification, to name a few. Bayesian image analysis can improve image quality, by balancing a priori expectations of image characteristics, with a model for the noise process via Bayes Theorem. We have previously given a reformulation of the conventional Bayesian image analysis paradigm in Fourier space, i.e. the prior distribution (the prior) and likelihood are given in terms of spatial frequency signals. By specifying the Bayesian model in Fourier space, spatially correlated priors, that are relatively difficult to model and compute in conventional image space, can be efficiently modeled as a set of independent processes across Fourier space. The originally inter-correlated and high-dimensional problem in image space is thereby broken down into a series of (trivially parallelizable) independent one-dimensional problems. In this paper we adapt this Fourier space process into a data-driven framework in which the Fourier space priors are built empirically from a database of images and then used to enhance future images. We will describe the data-driven Bayesian image analysis in Fourier space (DD-BIFS) modeling approach, illustrate it’s computational efficiency and speed. Finally, we give specific applications of DD-BIFS to improve the quality of arterial-spin-labeling (ASL) perfusion images via a database of human brain positron emission tomography (PET) images.
21 Oct 2011-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, a C++-based software was developed to carry out a set of measurements on the full-equipped chambers of the LHCb muon detector, which is made of front-end control electronics, high-voltage supply and acquisition circuitry while the software, running on a PC, remotely controls each element of the system and implements a number of automatized procedures to assess the main characteristics of the chambers.
Abstract: In a detector with the complexity of the LHCb, where only for the muon system more than 1300 chambers, divided into 20 different types, will be used, resulting on more than 120 k channels to be readout, it is of crucial importance to study the many types of chambers to create a complete knowledge of the detector operation and to guarantee a high-quality performance during the experiment. To make it possible, a complete setup was built and a C++ based software was developed to carry out a set of measurements on the full-equipped chambers of the LHCb muon detector. The setup is made of front-end control electronics, high-voltage supply and acquisition circuitry while the software, running on a PC, remotely controls each element of the system and implements a number of automatized procedures to assess the main characteristics of the chambers. The main advantages of this system are its versatility and speed of measurement which are crucial to the experiment since there is the need to characterize every single chamber before final installation. Moreover, in this work it was proposed to measure the starting knee of the high-voltage operational plateau without the use of an external trigger by making use of the internal structure of the chambers. Two laboratories were prepared at CERN (European Laboratory for Particle Physics) to receive this system; one used to test chambers arrived from the CERN itself and the PNPI (Petersburg Nuclear Physics Institute) production sites, and one to test the chambers arrived from the INFN (National Institute of Nuclear Physics) production sites. In this document, the hardware and software setup will be presented together with the measurement-oriented implementations.
TL;DR: Schottky, Nyquist, and Johnson as mentioned in this paper investigated the provenance of bruits de souffle dans les tubes a vide and of l'effet de grenaille des resistance.
Abstract: Les auteurs rappellent d’abord l’importance de l’utilisation des sons a spectre continu en acoustique, et principalement en acoustique architecturale (I). Puis ils precisent la provenance des bruits de souffle dans les tubes a vide et de l’effet de grenaille des resistance (II, 1 et 2). Apres avoir rappele, sans les demontrer, les formules fondamentales de la theorie du bruit de fond, theorie faite a l’origine principalement parSchottky, Nyquist etJohnson, (II, 3 et 4), ils examinent le cas des tubes a atmosphere gazeuse (II, 5).
01 Jan 1980
TL;DR: The Hurst phenomenon, which has been an important subject of research and some controversy within the hydrological world and outside, is described and the associated theoretical treatment of the rescaled range is taken up.
Abstract: This chapter concerns properties of special significance in hydrology. In the general class of crossing properties, theoretical aspects of runs, run lengths and sums are explained, and their practical relevance is discussed. Reservoir storage analysis which follows includes the Rippl diagram and the concepts of deficit and range. In this context the Hurst phenomenon, which has been an important subject of research and some controversy within the hydrological world and outside, is described, and the associated theoretical treatment of the rescaled range is taken up. Fractional gaussian processes which maintain the Hurst effect over very long time spans are explained. The final sections pertain to models that generate fractional noise and the broken-line model which is outlined. To aid the practitioner, some computer subroutines are provided.
TL;DR: In this paper, the intersection points of a fixed planar curve with the nodal set of a translationally invariant and isotropic Gaussian random field were studied and the zeros of its normal derivative across the curve.
Abstract: We study the intersection points of a fixed planar curve $\Gamma$ with the nodal set of a translationally invariant and isotropic Gaussian random field $\Psi(\bi{r})$ and the zeros of its normal derivative across the curve. The intersection points form a discrete random process which is the object of this study. The field probability distribution function is completely specified by the correlation $G(|\bi{r}-\bi{r}'|) = $.
Given an arbitrary $G(|\bi{r}-\bi{r}'|)$, we compute the two point correlation function of the point process on the line, and derive other statistical measures (repulsion, rigidity) which characterize the short and long range correlations of the intersection points. We use these statistical measures to quantitatively characterize the complex patterns displayed by various kinds of nodal networks. We apply these statistics in particular to nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of special interest is the observation that for monochromatic random waves, the number variance of the intersections with long straight segments grows like $L \ln L$, as opposed to the linear growth predicted by the percolation model, which was successfully used to predict other long range nodal properties of that field.