DOI: 10.17586/2226-1494-2017-17-3-417-423


ON RESTORATION OF SMEARED COLOR IMAGES

V. S. Sizikov, A. K. Ilyin


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Article in Russian

For citation: Sizikov V.S., Ilyin A.K. On restoration of smeared color images. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2017, vol. 17, no. 3, pp. 417–423 (in Russian). doi: 10.17586/2226-1494-2017-17-3-417-423

Abstract

Subject of Research. The paper deals with the problem of a "usual" (not fast) and fast restoration of color smeared images based on solving the Fredholm integral equation of the first kind (ill-posed problem). Method. The equation is solved by the quadrature method with Tikhonov’s regularization. Two methods for processing of color images are considered: methods of component-wise and vector processing. Main Results. If a model image is processed and an algorithm is usual (not fast), then the regularization parameter ais chosen from the condition of restoration error minimum. If a real image is processed and an algorithm is fast, then to choose aand the value of smear Δ, we propose the fast method of "prepared matrix", realized within 1 second. But if a real image is processed and an algorithm is not fast, then we propose the method for estimating Δ (and the smear angle θ), based on the spectrum of smeared image, and ais selected by known methods. Practical Relevance. The presented algorithms can be used to restore color smeared images, e.g., images of fast moving objects (a car, an airplane) by mathematical and computer processing of smeared (and noisy) images. 


Keywords: smeared color image, integral equation, ill-posed problem, regularization, component-wise and vector processing methods, regularization parameter, smear, "prepared" matrix fast algorithm, spectral method, MATLAB.

Acknowledgements. This work was supported by the Russian Foundation for Basic Research (RFBR), grant No. 13-08-00442.

References
1.     Vasilenko G.I., Taratorin A.M. Image Restoration. Moscow, Radio i Svyaz' Publ., 1986, 304 p. (In Russian)
2.     Tikhonov A.N., Goncharskii A.V., Stepanov V.V. Inverse Problems of Photoimages Processing. In Ill-Posed Problems in Natural Science. Ed. A.N. Tikhonov, A.V. Goncharskii. Moscow, MSU Publ., 1987, pp. 185–195. (In Russian)
3.     Bates R.H.T., McDonnell M.J. Image Reconstruction and Recognition. Oxford, Clarendon Press, 1986.
4.     Methods of Computer Image Processing. Ed. V.A. Soifer. Moscow, Fizmatlit Publ., 2001, 784 p. (In Russian)
5.     Gruzman I.S., Kirichuk V.S., Kosykh V.P., Peretyagin G.I., Spektor A.A. Digital Image Processing in Information Systems. Novosibirsk, NSTU Publ., 2002, 352 p. (In Russian)
6.     D'yakonov V., Abramenkova I. MATLAB. Processing of Signals and Images. St. Petersburg, Piter Publ., 2002, 608 p. (In Russian)
7.     Gonzales R.C.,Woods R.E. Digital Image Processing. 2nd ed. Upper Saddle River, Prentice Hall, 2002, 793 p.
8.     Gonsales R.C., Woods R.E., Eddins S.L. Digital Image Processing Using MATLAB. Prentice Hall, 2004, 344 p.
9.     Hansen P.C., Nagy J.G., O’Leary D.P. Deblurring Images: Matrices, Spectra, and Filtering. Philadelphia, SIAM, 2006, 130 p.
10.  Sizikov V.S. Inverse Applied Problems and MatLab. St. Petersburg, Lan' Publ., 2011, 256 p. (In Russian).
11.  Shlikht G.Yu. Digital Processing of Color Images. Moscow, Ekom Publ., 1997, 336 p. (In Russian)
12.  Jähne B. Digital Image Processing. 6th ed. Berlin–Heidelberg–NY, Springer, 2005, 654 p.
13.  Yagola A.G., Koshev N.A. Restoration of smeared and defocused color images. Numerical Methods and Programming, 2008, vol. 9, pp. 207–212. (In Russian)
14.  Aref'eva M.V., Sysoev A.F. Fast regularizing algorithms for digital image recovery.Numerical Methods and Programming, 1983, no. 39, pp. 40–55. (In Russian)
15.  Sizikov V.S., Ekzemplyarov R.A. Preliminary and subsequent filtering of noise in image restoration algorithms. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2014, no. 1, pp. 112–122. (In Russian)
16.  Tikhonov A.N., Arsenin V.Ya. Methods for Solving Ill-Posed Problems. 3rd ed. Moscow, Nauka Publ., 1986, 288 p. (In Russian)
17.  Verlan' A.F., Sizikov V.S. Integral Equations: Methods, Algorithms, Programs. Kiev, Naukova Dumka, 1986, 544 p. (In Russian).
18.  Engl H.W., Hanke M., Neubauer A. Regularization of Inverse Problems. Dordrecht, Kluwer, 1996, 328 p.
19.  Voskoboinikov Yu.E., Mukhina I.N. Local regularizing restoration algorithm of the contrast signals and images. Avtometriya, 2000, no. 3, pp. 45–53. (In Russian)
20.  Sizikov V.S., Kir'yanov K.A., Ekzemplyarov R.A. Two fast algorithms for restoration of smeared images. Journal of Instrument Engineering, 2013, vol. 56, no. 10, pp. 24–30. (In Russian)
21.  Sizikov V.S. Estimating the point-spread function from the spectrum of a distorted tomographic image.Journal of Optical Technologies, 2015, vol. 82, no. 10, pp. 655–658. doi: 10.1364/JOT.82.000655
22.  Sizikov V.S. Spectral method for the point-scattering function estimation in the problem of eliminating image distortions. Journal of Optical Technologies, 2017, vol. 84, no. 2,
pp. 36–44.
23.  Donatelli M., Estatico C., Martinelli A., Serra-Capizzano S. Improved image deblurring with anti-reflective boundary conditions and re-blurring. Inverse Problems, 2006, vol. 22, no. 6, pp. 2035–2053. doi: 10.1088/0266-5611/22/6/008
24.  Sidorov D.N. Methods of Analysis of Integral Dynamic Models: Theory and Applications. Irkutsk, ISU Publ., 2013, 293 p. (in Russian)
Sidorov D. Integral Dynamical Models: Singularities, Signals and Control. Singapore-London, World Scientific Publ., 2014, 243 p.
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