Ergodic properties of fractional Langevin motion with spatial correlated noise

ABSTRACT In this paper, we investigate the impact of correlated noise on fast radio burst (FRB) searching. We found that (1) the correlated noise significantly increases the false alarm probability; (2) the signal-to-noise ratios (S/N) of the false positives become higher; (3) the correlated noise also affects the pulse width distribution of false positives, and there will be more false positives with wider pulse width. We use 55-h observation for M82 galaxy carried out at Nanshan 26m radio telescope to demonstrate the application of the correlated noise modelling. The number of candidates and parameter distribution of the false positives can be reproduced with the modelling of correlated noise. We will also discuss a low S/N candidate detected in the observation, for which we demonstrate the method to evaluate the false alarm probability in the presence of correlated noise. Possible origins of the candidate are discussed, where two possible pictures, an M82-harboured giant pulse and a cosmological FRB, are both compatible with the observation.

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Forgery Detection in Digital Images by Multi-Scale Noise Estimation

Journal of Imaging ◽

10.3390/jimaging7070119 ◽

2021 ◽

Vol 7 (7) ◽

pp. 119

Author(s):

Marina Gardella ◽

Pablo Musé ◽

Jean-Michel Morel ◽

Miguel Colom

Keyword(s):

Noise Model ◽

Correlated Noise ◽

Forgery Detection ◽

Color Channel ◽

Image Block ◽

Multi Scale ◽

Compressed Images ◽

Inconsistency Analysis ◽

Highly Correlated ◽

The Moment

A complex processing chain is applied from the moment a raw image is acquired until the final image is obtained. This process transforms the originally Poisson-distributed noise into a complex noise model. Noise inconsistency analysis is a rich source for forgery detection, as forged regions have likely undergone a different processing pipeline or out-camera processing. We propose a multi-scale approach, which is shown to be suitable for analyzing the highly correlated noise present in JPEG-compressed images. We estimate a noise curve for each image block, in each color channel and at each scale. We then compare each noise curve to its corresponding noise curve obtained from the whole image by counting the percentage of bins of the local noise curve that are below the global one. This procedure yields crucial detection cues since many forgeries create a local noise deficit. Our method is shown to be competitive with the state of the art. It outperforms all other methods when evaluated using the MCC score, or on forged regions large enough and for colorization attacks, regardless of the evaluation metric.

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Ergodic Properties of Multi-Dimensional Subtractive Algorithms

Analytic and Probabilistic Methods in Number Theory ◽

10.1515/9783112314234-013 ◽

1992 ◽

pp. 91-100

Keyword(s):

Ergodic Properties

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Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2020.123 ◽

2020 ◽

pp. 1-14

Author(s):

SHOTA OSADA

Keyword(s):

Point Processes ◽

Duke Math ◽

Random Point ◽

Determinantal Point Processes ◽

Fredholm Determinants ◽

Poisson Point Processes ◽

Translation Invariant ◽

Ergodic Properties ◽

Tree Representations ◽

Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

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