Using Fractional Gaussian Noise Models in Orbit Determination

2003 ◽  
Vol 26 (4) ◽  
pp. 593-607
Author(s):  
Winston C. Chow ◽  
Paul W. Schumacher
Keyword(s):  
Gaussian Noise ◽  
Orbit Determination ◽  
Fractional Gaussian Noise ◽  
Noise Models

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

scholarly journals Second-order total generalized variation based model for restoring images with mixed Poisson — Gaussian noise

2021 ◽  
pp. 20-32
Author(s):  
Cong Pham ◽  
Thi Thu Thao Tran ◽  
Thanh Cong Nguyen ◽  
Duc Hoang Vo
Keyword(s):  
Gaussian Noise ◽  
High Efficiency ◽  
Gaussian Model ◽  
Second Order ◽  
Total Generalized Variation ◽  
Proposed Model ◽  
Total Variation Model ◽  
Alternating Minimization Algorithm ◽  
Generalized Variation ◽  
Noise Models

Introduction: A common problem in image restoration is image denoising. Among many noise models, the mixed Poisson-Gaussian model has recently aroused considerable interest. Purpose: Development of a model for denoising images corrupted by mixed Poisson-Gaussian noise, along with an algorithm for solving the resulting minimization problem. Results: We proposed a new total variation model for restoring an image with mixed Poisson-Gaussian noise, based on second-order total generalized variation. In order to solve this problem, an efficient alternating minimization algorithm is used. To illustrate its comparison with related methods, experimental results are presented, demonstrating the high efficiency of the proposed approach. Practical relevance: The proposed model allows you to remove mixed Poisson-Gaussian noise in digital images, preserving the edges. The presented numerical results demonstrate the competitive features of the proposed model.

scholarly journals Sensitivity of the General Linear Model to Assumptions

2020 ◽  
Vol 6 (5) ◽  
pp. 21-25
Keyword(s):  
Linear Model ◽  
Gaussian Noise ◽  
Linear Models ◽  
General Linear Model ◽  
White Gaussian Noise ◽  
General Linear ◽  
Optimal Estimator ◽  
Significant Performance ◽  
Non Gaussian ◽  
Noise Models

Non-Gaussian noise often causes in significant performance abatement for systems which are designed using Gaussian assumption. This report challenges the question of General Linear Model with White Gaussian Noise assumption in order to define the sensitivity of the performance of an optimal estimator. Gaussian noise models provide an important role in many signal processing applications. The Laplacian and Uniform signal are two worthy examples of noise that can be compared to the White Gaussian Noise, though the sensitivity which can be compared with any non-Gaussian. White Gaussian Noise has been considered for General Linear Models and deviation from whiteness would affect on our estimates under different circumstances. Moreover, new assumptions have been considered to generate different type of signals in order to evaluate the sensitivity of the General Linear Model.

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