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.
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TL;DR: In this article, the first order probability density functions of the sums of N independent sinusoidal waves having random amplitudes and phases in additive Gaussian noise are studied for the cases where N is fixed and where N in Poisson distributed.
10 citations
22 Jan 2013
TL;DR: This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family.
Abstract: Magnitude magnetic resonance (MR) images are noise-contaminated measurements of the true signal, and it is important to assess the noise in many applications. A recently introduced approach models the magnitude MR datum at each voxel in terms of a mixture of up to one Rayleigh and an a priori unspecified number of Rice components, all with a common noise parameter. The Expectation-Maximization (EM) algorithm was developed for parameter estimation, with the mixing component membership of each voxel as the missing observation. This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family. Both the EM algorithm and variance estimation are then fairly straightforward without any need for potentially unstable numerical optimization methods. Compared to local neighborhood- and wavelet-based noise-parameter estimation methods, the new EM-based approach is seen to perform well not only in simulation experiments but also on physical phantom and clinical imaging data.
10 citations
TL;DR: In this paper, a mesoscopic vectorial order parameter is constructed through phase transitions in cortical populations that condense the background activity through spontaneous symmetry breaking, leading to a null spike in which the microscopic activity is uniformly disordered (symmetric).
10 citations
TL;DR: In this article, the authors used principal component analysis (PCT) to generate statistically independent hydrodynamic load and response values, as opposed to time simulation technique that leads to correlated response values.
10 citations
TL;DR: In this paper, the authors present an analysis of these modified statistics and demonstrate them with experimental results from Bedlam, a new digital backend for the Parkes radio telescope, which is used to detect and characterise a transient event with a duration comparable to the inverse bandwidth.
Abstract: The digital record of the voltage in a radio telescope receiver, after frequency conversion and sampling at a finite rate, is not a perfect representation of the original analog signal. To detect and characterise a transient event with a duration comparable to the inverse bandwidth it is necessary to compensate for these effects, altering the statistical properties of the signal and making it difficult to determine the significance of a potential detection. We present an analysis of these modified statistics and demonstrate them with experimental results from Bedlam, a new digital backend for the Parkes radio telescope.
10 citations