ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

vol 63 / January, 2020

DOI 10.17586/0021-3454-2019-62-4-379-386

UDC 621.397.3:519.642.3


V. S. Sizikov
ITMO University, Saint Petersburg, 197101, Russian Federation; Professor

A. A. Sergienko
Университет ИТМО, ITMO University, Educational Center of Graphic Technologies;

ITMO University, Department of Graphic Technologies;

Abstract. The spectral method is developed for estimating the parameters of the point-spread function (PSF) in the problem of restorating the distorted (smeared, defocused) im-ages. The method is based on the analysis of a spectrum, or the Fourier transform (FT) of a distorted image. This method makes it possible to estimate the PSF parameters: the angle θ and magnitude Δ of image smearing, as well as the size  of the image defocusing spot. This enhances the image restoration accuracy. The smeared image spectrum is compressed in the smearing direction, and this makes it possible to estimate θ and Δ. The defocused image spectrum is also compressed, and more strongly, the larger the defocusing spot. A new estimates are obtained for the smearing parameters θ and Δ using the Nyquist frequency and for the defocusing parameter  using the Bessel function. The results of applying this method to image processing are presented. The developed technique can be used to enhance the accuracy of smeared and defocused image restoration via their mathematical processing by solving the integral equations.
Keywords: image distortions (smearing, defocusing), point-spread function, distortion parameters, Fourier spectrum of distorted image, Nyquist frequency, Bessel function,


1. Bates R.H.T., McDonnell M.J. Image Restoration and Reconstruction, Oxford, Oxford U. Press, 1986, 336 p. 2. Gruzman I.S., Kirichuk V.S., Kosykh V.P., Peretyagin G.I., Spektor A.A. Digital Image Processing in Information Systems, Novosibirsk, 2002, 352 p. (in Russ.). 3. Gonzalez R.C., Woods R.E. Digital Image Processing, 2nd ed., Upper Saddle River, Prentice Hall, 2002, 793 p. 4. Jähne B. Digital Image Processing, Berlin–Heidelberg, Springer-Verlag, 2005, 584 p. 5. Sizikov V.S. Inverse Applied Problems and MatLab, St. Petersburg, 2011, 256 p. (in Russ.). 6. Sizikov V.S. Direct and Inverse Problems of Image Restoration, Spectroscopy and Tomography with MatLab, St. Petersburg, 2017, 412 p. (in Russ.). 7. Tikhonov A.N., Goncharsky A.V., Stepanov V.V. Ill-Posed Problems in Natural Science, Moscow, 1987, pp. 185–195. (in Russ.). 8. Soifer V.A., ed., Methods of Computer Image Processing, Moscow, 2001, 784 p. (in Russ.). 9. Gonsales R.C., Woods R.E., Eddins S.L. Digital Image Processing using MATLAB, New Jersey, Prentice Hall, 2004, 609 p. 10. Hansen P.C., Nagy J.G., O’Leary D.P. Deblurring Images: Matrices, Spectra, and Filtering, Philadelphia, SIAM, 2006, 130 p. 11. Sizikov V.S., Sergienko A.A., Rushchenko N.G. Journal of Instrument Engineering, 2019, no. 1(62), pp. 69–77. (in Russ.). 12. Voskoboinikov Yu.E. Optoelectronics, Instrumentation, and Data Processing, 2000, no. 6(43), pp. 489–499. DOI: 10.3103/S8756699007060015. 13. Sizikov V.S., Ékzemplyarov R.A. Journal of Optical Technology, 2013, no. 1(80), pp. 28–34. DOI: 10.1364/JOT.80.000028. 14. D'yakonov V., Abramenkova I. MATLAB. Processing of Signals and Images, St. Petersburg, 2002, 608 p. (in Russian). 15. Voskoboinikov Yu.E., Mukhina I.N. Optoelectronics, Instrumentation, and Data Processing, 2000, no. 3, рp. 41–48. 16. Donatelli M., Estatico C., Martinelli A., Serra-Capizzano S. Inverse Problems, 2006, vol. 22, рр. 2035–2053. DOI: 10.1088/0266-5611/22/6/008. 17. Donatelli M., Huckle T., Mazza M., Sesana D. Numerical Algorithms, 2016, no. 2(72), pp. 341–361. DOI: 10.1007/s11075-015-0047-x. 18. Sidorov D.N. Methods for Analysis of Integral Dynamic Models: Theory and Applications, Irkutsk, 2013, 293 p. (in Russian). 19. Sidorov D. Integral Dynamical Models: Singularities, Signals and Control, Singapore–London,World Sci. Publ., 2014, 243 p. 20. Sizikov V.S. Journal of Optical Technology, 2017, no. 2(84), pp. 95–101. DOI: 10.1364/JOT.84.000095. 21. Sizikov V.S. Journal of Optical Technology, 2015, no. 10(82), pp. 655–658. DOI: 10.1364/JOT.82.000655. 22. Sizikov V.S., Stepanov A.V., Mezhenin A.V., Burlov D.I., Éksemplyarov R.A. Journal of Optical Technology, 2018, no. 4(85), pp. 203–210. DOI: 10.1364/JOT.85.000203. 23. Vasilenko G.I., Taratorin A.M. Image Restoration, Moscow, 1986, 304 p. (in Russ.). 24. Korn G.A., Korn T.M. Mathematical Handbook for Scientists and Engineers, NY, McGraw-Hill, 1961. 25. Bronshtein I.N., Semendyaev K.A. Mathematical Handbook for Engineers and Students of Technical Colledges, 13th ed., Moscow, 1986, 544 p. (in Russian). 26. Bracewell R.N. The Hartley Transform, NY, Oxford University Press, 1986, 168 p. 27. Antonova T.V. Numerical Analysis and Applications, 2015, no. 2(8), pp. 89–100. DOI: 10.1134/S1995423915020019.