ИСТИНА

We study a problem of designing a two-dimensional Point Spread Function (PSF) with a given radius R. Such a function will be optimal for estimating an unknown signal f from an observation g = a * f +n. Here the PSF a represents a convolution-type distortion and n is random noise. It is shown that if the additive noise is uncorrelated, then the optimization problem reduces to a one-dimensional Fredholm equation of the second kind on [0;R]. There are many ways to solve such problems numerically. However, it might be more natural to construct the PSF r in a certain finite-dimensional class of functions from the very beginning. Such a problem reduces to a set of linear equations. This technique is then generalized to the case when the PSF a is not known precisely.