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In this paper, image-restoration techniques based upon a regression model are analyzed and verified by computer simulation. A regression model is formulated to describe image blurring, additive noise, physical image sampling, and quadrature representation. Classical estimation methods utilized for image restoration are described and related to one another. Restorations obtained by these classical techniques are shown to be poor because of noise disturbances and the ill conditioning of the image-degradation regression model. Constrained restoration methods which avoid ill conditioning problems are introduced. Computer simulations demonstrate that a boundedness constraint on the brightness of a reconstructed image provides significantly improved restorations as compared to unconstrained methods.