Reduction of correlated noise using a library of orthonormal bases

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.

Download Full-text

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0291 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Wei Jiang ◽

Zhong Chen ◽

Ning Hu ◽

Yali Chen

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Reproducing Kernel ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

Kernel Space ◽

Reproducing Kernel Space ◽

Orthonormal Bases ◽

Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

Download Full-text

Modified Wilson Orthonormal Bases

Sampling Theory, Signal Processing, and Data Analysis ◽

10.1007/bf03549473 ◽

2007 ◽

Vol 6 (2) ◽

pp. 223-235

Author(s):

Piotr Wojdyłło

Keyword(s):

Orthonormal Bases

Download Full-text

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.

Download Full-text