UDC 004.932:519.64
INVESTIGATION OF THE REGULARIZATION METHOD FOR RESTORING BLURRED IMAGES
A. I. Novikov, Dr. Sc. (Tech.), associate professor, department of higher mathematics, RSREU, Ryazan, Russia;
orcid.org/0000-0002-8166-8234, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
N. O. Shamin, student of RSREU, Ryazan, Russia;
orcid.org/0000-0001-9175-9095, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The aim of the work is investigation of regularization method to reconstruct blurred one-dimensional and two-dimensional images with different features in the core and right-hand side of the Fredholm integral equation of the first kind of convolution type. The Euler equation was used as the basis of computational algorithm, which was reduced on a discrete grid to the system of linear algebraic equations with Toeplitz basic SLAE matrix. Studies of one-dimensional and two-dimensional images with inaccurately defined core of the equation and with additive noise superimposed on the blurred signal observed are carried out. The results obtained allow us to develop recommendations for processing blurred images.
Key words: integral equation, ill-posed problem, equation core, stabilizing functional, Euler equation, parametric family of solutions, optimal solution.