Abstract
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.
© 2009 Optical Society of America
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