scholarly journals Method of Constructing a Nonlinear Approximating Scheme of a Complex Signal: Application Pattern Recognition

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 737
Author(s):  
Oksana Mandrikova ◽  
Bogdana Mandrikova ◽  
Anastasia Rodomanskay
Keyword(s):  
Noise Suppression ◽  
A Priori ◽  
Noisy Data ◽  
Adaptive Threshold ◽  
Complex Signal ◽  
A Priori Information ◽  
Threshold Functions ◽  
Useful Signal ◽  
Natural Data ◽  
Priori Information

A method for identification of structures of a complex signal and noise suppression based on nonlinear approximating schemes is proposed. When we do not know the probability distribution of a signal, the problem of identifying its structures can be solved by constructing adaptive approximating schemes in an orthonormal basis. The mapping is constructed by applying threshold functions, the parameters of which for noisy data are estimated to minimize the risk. In the absence of a priori information about the useful signal and the presence of a high noise level, the use of the optimal threshold is ineffective. The paper introduces an adaptive threshold, which is assessed on the basis of the posterior risk. Application of the method to natural data has confirmed its effectiveness.

An optimal regularization method for convolution equations on the sourcewise represented set

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Ye Zhang ◽  
Dmitry V. Lukyanenko ◽  
Anatoly G. Yagola
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
A Priori ◽  
Noisy Data ◽  
Optimal Recovery ◽  
Multidimensional Case ◽  
A Priori Information ◽  
Ill Posed ◽  
Priori Information ◽  
Convolution Equations

AbstractIn this article, we consider an inverse problem for the integral equation of the convolution type in a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a priori information (sourcewise representation) based on optimal recovery theory we propose a new method. The regularization and optimization properties of this method are proved. An optimal minimal a priori error of the problem is found. Moreover, a so-called optimal regularized approximate solution and its corresponding error estimation are considered. Efficiency and applicability of this method are demonstrated in a numerical example of the image deblurring problem with noisy data.

Application of Computer Modelling in Adaptive Compensation of Interferences on Global Navigation Satellite Systems

2019 ◽  
pp. 339-380 ◽  
Author(s):  
Valerian Shvets ◽  
Svitlana Ilnytska ◽  
Oleksandr Kutsenko
Keyword(s):  
A Priori ◽  
Inverse Correlation ◽  
Global Navigation Satellite Systems ◽  
Navigation Satellite ◽  
A Priori Information ◽  
Satellite Systems ◽  
Useful Signal ◽  
Global Navigation ◽  
Priori Information ◽  
Global Navigation Satellite

Modern society is characterized by the increased use of global navigation satellite systems (GNSS), which is inseparably linked with the interference immunity ensurance. The most effective way to protect against interferences is an introduction into the receiver structure of adaptive interference compensators. However, the most of proposed methods have been designed for radiolocation and communication and use a priori information about the transmitted signal. Since as structure of GNSS signal differs from the radar and communication systems, GNSS does not know the time-frequency structure of the useful signal in advance, which excludes the possibility of using a number of widely known methods. In this chapter, the authors propose a method, which does not use a priori information about a useful signal, and a new direct method for calculating the inverse correlation matrix of interference in adaptive antennas of interferences compensators.

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