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 paper, the authors derived a general theoretical framework for fluctuation analysis of optical imaging data on faint galaxy fields, in particular on fields containing rich clusters of galaxies, in an attempt to determine the Schechter luminosity function of the dwarf galaxies that dominate the statistics at this magnitude range.
Abstract: ABSTRA C T It is evident that considerable information exists in astronomical data below the threshold for the detection of individual sources (perhaps set for a ‘5s ’ total detection, or for isophotal detection thresholds of ‘2s ’ above the sky background), and that such information, if descriptive of an underlying population of objects characterized by a relatively small parameter set, could in principle be used to set constraints on these parameters. We therefore derive a general theoretical framework for fluctuation analysis (after the radio astronomers’ ‘P(D)’ analysis) of optical imaging data on faint galaxy fields, in particular; on fields containing rich clusters of galaxies, in an attempt to determine the Schechter luminosity function of the dwarf galaxies that dominate the statistics at this magnitude range.
4 citations
TL;DR: Results show that the proposed model not only provides a good prediction performance but also leads to the optimization of the end-to-end chain in terms of accuracy and robustness, setting the ground for its generalization to different and more complex scenarios.
Abstract: Validation and accuracy assessment are themain bottlenecks preventing the adoption of image processing algorithms in the clinical practice. In the classical approach, a posteriori analysis is performed through objective metrics. In this work, a different approach based on Petri nets is proposed. The basic idea consists in predicting the accuracy of a given pipeline based on the identification and characterization of the sources of inaccuracy. The concept is demonstrated on a case study: intrasubject rigid and affine registration of magnetic resonance images. Both synthetic and real data are considered. While synthetic data allow the benchmarking of the performance with respect to the ground truth, real data enable to assess the robustness of the methodology in real contexts as well as to determine the suitability of the use of synthetic data in the training phase. Results revealed a higher correlation and a lower dispersion among the metrics for simulated data, while the opposite trend was observed for pathologic ones. Results show that the proposed model not only provides a good prediction performance but also leads to the optimization of the end-to-end chain in terms of accuracy and robustness, setting the ground for its generalization to different and more complex scenarios.
4 citations
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TL;DR: The aim of this chapter is to provide a review of the theory and modeling of coastal waves in the context of modeling nearshore morphodynamic processes, with a focus on the shoaling and breaking of random waves in shallow water.
Abstract: The aim of this chapter is to provide a review of the theory and modeling of coastal waves in the context of modeling nearshore morphodynamic processes. The first section deals with linear wave theory, with a focus on the shoaling and breaking of random waves in shallow water. The second section reviews the important nonlinear aspects of nearshore wave motion. The third section describes the nature and origins of long-period waves, with periods in the range 20–200 s. The chapter ends by emphasizing the importance of feedback between waves and evolving morphology in creating nearshore morphological features.
4 citations