28 March 1995 Optimal nonlinear restoration of random object using its linearly formed image
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Abstract
We chose the optimal method of nonlinear restoration by probabilistic approaches. As a criterium for the optimal choice, it is mean-squared-value of the restoration error. As prior information about random object and noise, there are autocorrelation functions of the object and noise. We are using unknown strictly monotonous nonlinear operator to construct a broad multitude of nonlinear methods for random object restoration. The reconstruction process consists of carrying out the recurrent scheme with proved convergence. The criterium for quality of solution is based on the error probability for object restoration to exceed any previously settled value. The solution of this problem is received for an isoplanatic imaging system under the assumption that the point-sampled spectra of the initial object and noise are independent. This analytical solution is then used as the first approximation for solution of the general problem. We have derived the recurrent scheme for the numerical solution of this task. The recurrent process is converging to the solution of a linear imaging equation.
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Dmitry V. Dovnar, Konstantin G. Predko, "Optimal nonlinear restoration of random object using its linearly formed image", Proc. SPIE 2424, Nonlinear Image Processing VI, (28 March 1995); doi: 10.1117/12.205215; https://doi.org/10.1117/12.205215
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