ISSN 1991-2927
 

ACP № 3 (61) 2020

Author: "Marina Vitalievna Samoilenko"

Marina Vitalevna Samoilenko, Candidate of Science in Engineering, Associate Professor; graduated from Moscow Aviation Institute and the Moscow Institute of Physics and Engineering; Associate Professor at Moscow Aviation Institute (National Research University); an author of articles, monographs, and inventions in the field of signal and image processing. e-mail: Samoi.Mar@mail.ru.M. Samoilenko

Stochastic Matrix-Iterative Method And Its Application In the Images Processing 57_6.pdf

The article deals with a new method for solving the set of linear algebraic equations (SLAE). It is a stochastic matrixiterative method. This method is designed for solving a wide class of problems in which measurement errors are presented. When the SLAE is represented as a vector-matrix equation, the desired variables are united into vector-original. The applicability of the method is limited by the type of the vector-original being restored: the main part of its components should be equal to the known background value, and a limited number of components should exceed this value. When processing images, this condition means that we have a limited number of bright objects on a constant background.
The application of the proposed method is been demonstrated on the examples of restoration of the blurry and noised images. The task is converted to SLAE, in which the vector-image is a row-column scan of the distorted image, and the being reconstructed vector-original is the row-column scan of the original undistorted image. Computer simulation have been performed in the MATLAB medium, which made it possible to determine the optimal parameters of the stochastic matrixiterative method and to demonstrate its advantages under conditions of additive noise.
Such conditions are the small image fullness with objects and a large fullness with background values. The influence of additive noise and a priori uncertainty were not considered.

Stochastic matrix-iterative method, matrix-iterative method, SLAE, additive noise, image restoration, point spread function.

2019_ 3

Sections: Information systems

Subjects: Information systems.



Marina Viltalevna Samoilenko, Moscow Aeronautical Institute of National Research University, Candidate of Science in Engineering, Associate Professor; graduated from Moscow Aeronautical Institute and Moscow Institute of Physics and Technologies; Associate Professor at Moscow Aeronautical Institute of National Research University; an author of monographs, articles, and inventions; scientific interests are in the field of signal and image processing. [e-mail: Samoi.Mar@mail.ru]M. Samoilenko

Matrix-Iterative Method of the Blurred Images Restoration 56_11.pdf

A new method of the picture-original restoration from the blurred image is proposed. This method is based on the matrixiterative method developed by the author for solving the simultaneous linear algebraic equations. When implementing the image-restoration method, the author uses a prior information specified. It is assumed that the intensity of minimum background values of this image as well as the point spread function are known. The task of image restoration is resulted in the solution of an underdetermined system of linear algebraic equations. A pseudoinverse technique of its matrix is a known solution of the simultaneous linear algebraic equations. The well-known image restoration method based on this solution is also given. The author compares the image restoration by the use of this well-known method and a new matrix-iterative method based on computer simulating. It is shown that the matrixiterative method provides almost exact restoration under certain conditions. Such condition is a low occupation level of an image being filled up with objects if there is a high occupation level of an image being filled up with background values. The additive noise impact and an expected uncertainty were not considered.

Simultaneous linear algebraic equations, matrix-iterative method, image restoration, point spread function, pseudoinverse technique.

2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Artificial intelligence.



Marina Vitalevna Samoilenko, Moscow Aeronautical Institute, Candidate of Science in Engineering; graduated from Moscow Aeronautical Institute and Moscow Institute of physics and Technologies; Associate Professor at Moscow Aeronautical Institute (of National Research University); an author of articles, monographs and inventions; scientific interests are in the field of signal and image processing. [e-mail: Samoi.Mar@mail.ru]M. Samoilenko

Reconstruction of the Point Spatial Coordinates in the Case of Normal Stereo Photography 55_11.pdf

The article presents a solution for the problem of a point spatial coordinates reconstructing in a base coordinate system by its two stereo images. Author solves the problem for the case of identical cameras application which optical axes are mutually parallel and orthogonal to the stereoscopic basis. This taking photo is called in photogrammetry as a normal photographing. Author provides a computational simplicity of a point spatial position recovery algorithm. But in classical photogrammetry this computational simplicity is provided only under additional restrictions: cameras should locate at the same height, images should be horizontal and the base of stereoscopy - parallel to the horizontal axis of the base coordinate system. For another camera positions, it will be necessary to use additional spatial similarity transforms which complicate computations.Solution presented in the article differs from the photogrammetric method by its universality: neither additional conditionsare imposed to the positions of the cameras and images. And at the same time, it has computational simplicity comparable with the photogrammetric method of normal photography with additional restrictions. Methodologically, decision presented in the article is based completely on the application of vector-matrix approach from the problem formulation up to the final result. Structurally, it differs from the photogrammetric method by its symmetry with respect to of the cameras and images parameters: cameras are equivalent when determining a point spatial coordinates, while the photogrammetric solution is based on the coordinates on one image, the other one is used for the scaling factor determination.The universality of the presented solution and its computational simplicity are proved by the results of computer experiments.

Stereo images, point spatial coordinates, central projecting, vector-matrix equation, photogrammetry, normal photographing.

2019_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.



Marina Vitalievna Samoilenko, Moscow Aviation Institute (National Research University), Candidate of Engineering; graduated from Moscow Aviation Institute and Moscow Institute of Physics and Technology; Associate Professor at Moscow Aviation Institute (National Research University); involved in developing the tomographic approach to signal processing; an author of 11 patents for inventions, 2 monographs, and 9 articles. [e-mail: Samoi.Mar@mail.ru]M. Samoilenko

Tomographic Method of Signal Restoration After Passing Through the Filter With the Known Response 000_3.pdf

The method of the filter input signal restoration by the measured output signal and the pulse response is proposed in the article. The known method of the input signal restoration is inverse filtering, which inevitably distorts the restored signal because of the effect of power leakage into the adjacent frequency range or of the inability to calculate the infinite spectrum of the input signal by dividing the spectrum of the output signal on transmission function. The proposed method doesn’t need transformation to spectrums. It is based on the tomographic approach in signal processing developed by the author. According to the method, the solution is sought through the restoration of the required function (of the input signal) by a set of its integrals values received under differing conditions of integration. The values of the output signal measured at discrete moments are used as such values. A set of output signals (integrals) forms a depiction, which is used for the following restoration of the original - the input signal. The received mathematical expressions make it possible to restore it in a discrete form as a vector. The restore matrix used in calculations is formed on the basis of discrete values of a filter pulse response and can be calculated a priori. After that, it’s enough to measure the output signal and multiply the vector composed of it on the pre-calculated matrix in operating status. The pre-selected discretization period may be changed to achieve greater accuracy or lesser processing time. The tomographic method makes it possible to restore continuous signals as well as solar pulses and pulse patterns. In order to illustrate it, the article gives some results of computer simulation.

Signal restoration, tomographic approach to signal processing, pulse response, converting matrix, restore matrix.

2017_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.


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