Reconstruction of smeared images by various methods

Римских М.В., Евсеев В.О., Сизиков В.С. Реконструкция смазанных изображений различными методами // Оптический журнал. 2007. Т. 74. № 11. С. 53–57.

Rimskikh M.V., Evseev V.O., Sizikov V.S. Reconstruction of smeared images by various methods [in Russian] // Opticheskii Zhurnal. 2007. V. 74. № 11. P. 53–57.

M. V. Rimskikh, V. O. Evseev, and V. S. Sizikov, "Reconstruction of smeared images by various methods," Journal of Optical Technology. 74 (11), 764-768 (2007). https://doi.org/10.1364/JOT.74.000764

This paper discusses the problem of reconstruction of smeared images. The problem reduces to solving a set of one-dimensional convolution-type integral Fredholm equations of the first kind. Two methods of solving such equations are compared: the method of Fourier transformation, and the method of quadratures (using the method of Tikhonov regularization in both cases). Numerical results are presented, and it is concluded that the method of quadratures is more efficient than the method of Fourier transformation.