Constructing FIR-filtres in a given parametrical class of frequency response for defocus correction
V.A. Fursov


Image Processing Systems Institute оf RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia

Full text of article: Russian language.


A problem of the restoration of defocused images is considered. For this purpose, we construct an FIR-filter by identifying the model from a special class of parameters with use of test images. The model of impulse response is defined in a class of univariate functions, which approximate the required frequency response in the radial direction. Samples of the two-dimensional impulse response are defined by discretization and the subsequent sample normalization. The approximation function class is defined so as to amplify low and suppress high spectrum frequencies. Important advantages of the method are high-quality image restoration and fast identification of filter's model due to the fact that the approximating function is determined by a small number of unknown parameters. In this article realization examples are given. These examples show the possibility of achieving the higher-quality restoration in comparison with the Wiener filter from the open-source image processing library OpenCV.

FIR-filter, impulse response, frequency response, image processing.

Fursov VA. Constructing FIR-filters for a given parametrical class of frequency response for defocus correction. Computer Optics 2016; 40(6): 878-886. DOI: 10.18287/2412-6179-2016-40-6-878-886.


  1. Pratt WK. Digital Image Processing. New York, Chichester, Brisbane, Toronto: John Wiley and Sons; 1978.
  2. Moreno C. Constructing FIR Digital Filters with valarry. Source: áñ.
  3. Ye W, Yu YJ. Greedy algorithm for the design of linear-phase fir filters with sparse coefficients / Circuits, Systems, and Signal Processing 2016; 35: 1427. DOI: 10.1007/s00034-015-0122-5.
  4. Soifer VA, ed. Computer Image Processing, Part II: Methods and algorithms. VDM Verlag; 2009.
  5. Kopenkov VN, Myasnikov VV. An algorithm for automatic construction of computational procedure of non-linear local image processing on the base of hierarchical regression [In Russian]. Computer Optics 2012; 36(2): 257-265.
  6. Fursov VA. Identification of distorting systems with monitoring of data capacity. 5-th International Workshop on Digital Image Processing and Computer Graphics. “Image Processing and Computer Optics”, Samara, Russia, Aug, 22-26, 1994. Pt 2.
  7. Fursov VA, Nikonorov AV, Bibikov SA, Yakimov PYu, Minaev EYu. Correction of distortions in color images based on parametric identification. Pattern Recognition and Image Analysis 2011; 21(2): 125-128. DOI: 10.1134/S1054661811020349.
  8. Shcherbakov МА, Panov AP. Nonlinear filtering with adaptation to local properties of the image. Computer Optics 2014; 38(4): 818-824.
  9. Arar S. FIR Filter Design by Windowing: Concepts and the Rectangular Window. Source: áhttp://www.allabout­­ter-design-by-windowing-part-i-concepts-and-rect/ñ.
  10. Petrou M, Petrou C. Image Processing: Fundamentals. 2nd ed. John Wiley& Sons Ltd; 2010. ISBN 978-0-470-74586-1.
  11. Bavrina AYu, Myasnikov VV, Sergeev AV. Method of parametric estimation of optoelectronic tract of remote sensed optical image formation [In Russian]. Computer Optics 2011, 35(4): 500-507.
  12. Koltsov PP. Image blur estimation [In Russian]. Computer Optics 2011, 35(1): 95-102.
  13. Nikonorov AV, Milyutkin MG, Fursov VA. Parallel implementation of 2D IIR-filters using image processing distributed systems [In Russian]. Numerical Methods and Programming. Scientific on-line open access journal 2010, 11(1): 88-94.
  14. Fursov VA. Construction of adaptive identification algorithms, using the estimates conformity principle. 11th International Conference on Pattern Recognition and Image Analysis: New Information Technologies (PRIA-11-2013). Samara, September 23-28, 2013. Conference Proceedings (Vol. I-II) 2013; 1: 22-25.
  15. Fursov VA. Constructing unified identification algorithms using a small number of observations for adaptive control and navigation systems. Proc SPIE 1997; 3087: 34-44. DOI: 10.1117/12.277217.
  16. Ljung L. System Identification. Theory for the User. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.; 1987. ISBN: 9780138816407.
  17. Dudgeon DE, Mersereau RM. Multidimensional digital signal processing. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.; 1984.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail:; Phones: +7 (846) 332-56-22, Fax: +7 (846) 332-56-20