On the extrapolation of optical image data

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Abstract
In this paper we show that the extrapolation of an image’s piece as well as the object-reconstruction problem are improperly posed in the sense that the solutions do not depend continuously on the data. We try to restore the stability for these problems introducing suitable additional constraints. In the present work we treat in detail only the extrapolation of the image data. At this purpose we use and illustrate two numerical methods, which are based on the doubly-orthogonality of the linear-prolate-spheroidal-functions. Finally a probabilistic approach to these questions is outlined.