Restoration of a blurred photographic image of a moving object obtained at the resolution limit

Objectives. When processing images of the Earth’s surface obtained from satellites, the problem of restoring a blurry image of a moving object is of great practical importance. The aim of this work is to study the possibility of improving the quality of restoration of blurry images obtained at the l...

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Main Authors: V. B. Fedorov, S. G. Kharlamov, A. I. Starikovskiy
Format: Article
Language:Russian
Published: MIREA - Russian Technological University 2023-08-01
Series:Российский технологический журнал
Subjects:
Online Access:https://www.rtj-mirea.ru/jour/article/view/739
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author V. B. Fedorov
S. G. Kharlamov
A. I. Starikovskiy
author_facet V. B. Fedorov
S. G. Kharlamov
A. I. Starikovskiy
author_sort V. B. Fedorov
collection DOAJ
description Objectives. When processing images of the Earth’s surface obtained from satellites, the problem of restoring a blurry image of a moving object is of great practical importance. The aim of this work is to study the possibility of improving the quality of restoration of blurry images obtained at the limit of the resolution of the camera.Methods. Digital signal processing methods informed by the theory of incorrect and ill-conditioned problems were used.Results. The proposed method for restoring a blurred photographic image of a moving object differs from traditional approaches in that the discrete convolution equation, to which the problem of restoring a blurred image is reduced, is obtained by approximating the corresponding integral equation based on the Kotelnikov interpolation series rather than on the traditional basis of the quadrature formula. In the work, formulas are obtained for calculating the kernel of the convolution obtained using the Kotelnikov interpolation series. The discrete convolution inversion problem, which belongs to the class of ill-posed problems, requires regularization. Results of traditional approaches to restoring blurred images using the quadrature formula with Tikhonov regularization and the proposed method based on the Kotelnikov interpolation series are compared. Although the quality of the blurred image restoration is almost the same in both cases, in the quadrature formula the blur value is expressed as an integer number of pixels, while, when using the Kotelnikov series, this value can also be specified in fractions of a pixel.Conclusions. The expediency of discretizing the convolution describing the image distortion of the blur type on the basis of the Kotelnikov interpolation series when processing a blurred image obtained at the limit of the resolution of the camera is demonstrated. In this case, the amount of blur can be expressed in fractions of a pixel. This situation typically arises when processing satellite photography of the Earth’s surface.
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spelling doaj-art-fd08b2be127e4e6db3fbdbfa7a182ae02025-08-20T02:53:53ZrusMIREA - Russian Technological UniversityРоссийский технологический журнал2782-32102500-316X2023-08-011149410410.32362/2500-316X-2023-11-4-94-104387Restoration of a blurred photographic image of a moving object obtained at the resolution limitV. B. Fedorov0S. G. Kharlamov1A. I. Starikovskiy2MIREA – Russian Technological UniversityMIREA – Russian Technological UniversityMIREA – Russian Technological UniversityObjectives. When processing images of the Earth’s surface obtained from satellites, the problem of restoring a blurry image of a moving object is of great practical importance. The aim of this work is to study the possibility of improving the quality of restoration of blurry images obtained at the limit of the resolution of the camera.Methods. Digital signal processing methods informed by the theory of incorrect and ill-conditioned problems were used.Results. The proposed method for restoring a blurred photographic image of a moving object differs from traditional approaches in that the discrete convolution equation, to which the problem of restoring a blurred image is reduced, is obtained by approximating the corresponding integral equation based on the Kotelnikov interpolation series rather than on the traditional basis of the quadrature formula. In the work, formulas are obtained for calculating the kernel of the convolution obtained using the Kotelnikov interpolation series. The discrete convolution inversion problem, which belongs to the class of ill-posed problems, requires regularization. Results of traditional approaches to restoring blurred images using the quadrature formula with Tikhonov regularization and the proposed method based on the Kotelnikov interpolation series are compared. Although the quality of the blurred image restoration is almost the same in both cases, in the quadrature formula the blur value is expressed as an integer number of pixels, while, when using the Kotelnikov series, this value can also be specified in fractions of a pixel.Conclusions. The expediency of discretizing the convolution describing the image distortion of the blur type on the basis of the Kotelnikov interpolation series when processing a blurred image obtained at the limit of the resolution of the camera is demonstrated. In this case, the amount of blur can be expressed in fractions of a pixel. This situation typically arises when processing satellite photography of the Earth’s surface.https://www.rtj-mirea.ru/jour/article/view/739blurred image of a moving objectresolutionimage restorationtikhonov regularizationinverse problemkotelnikov interpolation seriesedge effect
spellingShingle V. B. Fedorov
S. G. Kharlamov
A. I. Starikovskiy
Restoration of a blurred photographic image of a moving object obtained at the resolution limit
Российский технологический журнал
blurred image of a moving object
resolution
image restoration
tikhonov regularization
inverse problem
kotelnikov interpolation series
edge effect
title Restoration of a blurred photographic image of a moving object obtained at the resolution limit
title_full Restoration of a blurred photographic image of a moving object obtained at the resolution limit
title_fullStr Restoration of a blurred photographic image of a moving object obtained at the resolution limit
title_full_unstemmed Restoration of a blurred photographic image of a moving object obtained at the resolution limit
title_short Restoration of a blurred photographic image of a moving object obtained at the resolution limit
title_sort restoration of a blurred photographic image of a moving object obtained at the resolution limit
topic blurred image of a moving object
resolution
image restoration
tikhonov regularization
inverse problem
kotelnikov interpolation series
edge effect
url https://www.rtj-mirea.ru/jour/article/view/739
work_keys_str_mv AT vbfedorov restorationofablurredphotographicimageofamovingobjectobtainedattheresolutionlimit
AT sgkharlamov restorationofablurredphotographicimageofamovingobjectobtainedattheresolutionlimit
AT aistarikovskiy restorationofablurredphotographicimageofamovingobjectobtainedattheresolutionlimit