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


V. S. Sizikov, A. K. Ilyin

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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


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.

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