Abstract
Information about an object that is contained in its blurred image is usually extremely poor to obtain an accurate inverse solution. For this reason only somefunctionals of the object can be recovered, which give, in general, a more rough description. It is natural to choose, as functionals, theprincipal components, that is the linear combinations of the parameters estimates which contain the main bulk of information about the object. We show that the principal components can be found by orthogonal transform, based on the eigenvectors of theFisher informational matrix I. A simple way to compute the needed eigenvalues and eigenvectors ofI is considered. TheImage Randomness Test is applied to test the feasibility of an object's estimate. As a result, the stable estimate of the object can be constructed by using only the inner resources of the theory, without referring to the Bayes way of consideration.
An algorithm of image restoration is described, which takes into account both the photon noise and non-negativity of the object, and is valid for the space-variant Point Spread Function.
The same treatment can be applied to other inverse problems.
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Terebizh, V.Y., Biryukov, V.V. On the problem of stable image restoration. Astrophys Space Sci 218, 65–86 (1994). https://doi.org/10.1007/BF00658067
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DOI: https://doi.org/10.1007/BF00658067