Reconstructing blurred noisy images without using boundary conditions

Сизиков В.С., Римских М.В., Мирджамолов Р.К. Реконструкция смазанных и зашумленных изображений без использования граничных условий // Оптический журнал. 2009. Т. 76. № 5. С. 38–46.

Sizikov V.S., Rimskikh M.V., Mirdzhamolov R.K. Reconstructing blurred noisy images without using boundary conditions [in Russian] // Opticheskii Zhurnal. 2009. V. 76. № 5. P. 38–46.

V. S. Sizikov, M. V. Rimskikh, and R. K. Mirdzhamolov, "Reconstructing blurred noisy images without using boundary conditions," Journal of Optical Technology. 76 (5), 279-285 (2009). https://doi.org/10.1364/JOT.76.000279

This paper proposes a new approach to the problem of taking into account the intensities coming from points outside the given boundaries of an image. This is done in a number of references by introducing so-called boundary conditions (antireflection, etc.). This paper, instead of using boundary equations, proposes a truncation method that does not require the intensities beyond the image boundaries to be known. Based on the truncation method, the direct and inverse problems of image processing are presented. Fourier transformation with Tikhonov regularization and the method of quadratures (also with regularization) are used to solve the inverse problem of reconstructing a distorted image. Numerical illustrations are given that show that the technique proposed in this paper appreciably reduces the reconstruction error.

The research was supported by RFBR (grant No. 09-08-00034-а).