Small-angle-scattering-data treatment by the regularization method

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The application of Tikhonov's regularization method [Tikhonov & Arsenin (1977). Solution of Ill-Posed Problems. New York: Wiley] for the solution of ill-posed problems in small-angle-scattering-data treatment is considered. Simple regularization algorithms are proposed for solving convolution equations in data desmearing (slit-width and polychromaticity problems) as well as for polydispersity problems. A general indirect approach of data processing based on the regularization method is described. Comparison with other data-treatment methods is made.