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Joint estimation of parameters of the underlying background image and a spatially extended object with an unknown area

Keywords:

А.P. Trifonov – Dr.Sc. (Eng.), Professor, Head of Radiophysics Department, Honored Scientist of the Russian Federation, Voronezh State University. Е-mail: trifonov@phys.vsu.ru, trirad@mail.ru Yu.N. Pribytkov – Ph.D. (Phys.-Math.), Associate Professor, Assistant of Radiophysics Department, Vo-ronezh State University. Е-mail:ypribytkov@gmail.com


The paper considers the problem of joint parameter estimation of image and background, and the influence of an unknown area of the image on the accuracy of these estimates also analyzed. To describe the image of a spatially extended object and the background models of homogeneous Gaussian random fields were selected. Intensity and regular components of these fields are informational parameters to be estimated. Unknown non-information parameter in the model is the image area. To analyze the influence of unknown space on the accuracy of estimates and regular components of image and background intensities two approaches to the resolution of a priori uncertainty about the area were considered. At the first approach quasi likelihood algorithm is used, in which an unknown area is replaced by the intended value. Asymptotically exact expressions for the dispersion of quasi likelihood estimations are obtained. The analysis showed that the use of quasi likelihood approach may lead to inconsistent estimates of informational parameter. At the second approach a joint maximum likelihood estimate of the unknown parameters and area information is considered. Asymp-totically exact expressions for the dispersion of the joint maximum likelihood estimates are obtained. It is shown that the accuracy of the maximum likelihood estimates may significantly exceed the accuracy quasi likelihood estimates. Also it is found that the characteristics of the joint maximum likelihood estimates of the parameters of the image, the underlying background and an unknown image area asymptotically with increasing signal-to-noise ratio are invariant to the absence of a priori information about the image area. However, unlike quasi likelihood estimates maximum likelihood estimation can be realized only through a multi-channel image for an unknown area.
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