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Proceedings Paper

Research of generalized wavelet transformations of Haar correctness in remote sensing of the Earth
Author(s): Maretta Kazaryan; Mihail Shakhramanyan; Roumen Nedkov; Andrey Richter; Denitsa Borisova; Nataliya Stankova; Iva Ivanova; Mariana Zaharinova
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Paper Abstract

In this paper, Haar's generalized wavelet functions are applied to the problem of ecological monitoring by the method of remote sensing of the Earth. We study generalized Haar wavelet series and suggest the use of Tikhonov's regularization method for investigating them for correctness. In the solution of this problem, an important role is played by classes of functions that were introduced and described in detail by I.M. Sobol for studying multidimensional quadrature formulas and it contains functions with rapidly convergent series of wavelet Haar. A theorem on the stability and uniform convergence of the regularized summation function of the generalized wavelet-Haar series of a function from this class with approximate coefficients is proved. The article also examines the problem of using orthogonal transformations in Earth remote sensing technologies for environmental monitoring. Remote sensing of the Earth allows to receive from spacecrafts information of medium, high spatial resolution and to conduct hyperspectral measurements. Spacecrafts have tens or hundreds of spectral channels. To process the images, the device of discrete orthogonal transforms, and namely, wavelet transforms, was used. The aim of the work is to apply the regularization method in one of the problems associated with remote sensing of the Earth and subsequently to process the satellite images through discrete orthogonal transformations, in particular, generalized Haar wavelet transforms. General methods of research. In this paper, Tikhonov's regularization method, the elements of mathematical analysis, the theory of discrete orthogonal transformations, and methods for decoding of satellite images are used. Scientific novelty. The task of processing of archival satellite snapshots (images), in particular, signal filtering, was investigated from the point of view of an incorrectly posed problem. The regularization parameters for discrete orthogonal transformations were determined.

Paper Details

Date Published: 10 October 2017
PDF: 13 pages
Proc. SPIE 10427, Image and Signal Processing for Remote Sensing XXIII, 104271U (10 October 2017); doi: 10.1117/12.2278572
Show Author Affiliations
Maretta Kazaryan, Financial Univ. at Government of the Russian Federation (Russian Federation)
Mihail Shakhramanyan, Researching Institute “Aerocosmos” (Russian Federation)
Roumen Nedkov, Space Research and Technology Institute (Bulgaria)
Andrey Richter, Researching Institute “Aerocosmos” (Russian Federation)
Denitsa Borisova, Space Research and Technology Institute (Bulgaria)
Nataliya Stankova, Space Research and Technology Institute (Bulgaria)
Iva Ivanova, Space Research and Technology Institute (Bulgaria)
Mariana Zaharinova, Space Research and Technology Institute (Bulgaria)

Published in SPIE Proceedings Vol. 10427:
Image and Signal Processing for Remote Sensing XXIII
Lorenzo Bruzzone, Editor(s)

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