Unbiased image reconstruction as an inverse problem

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Abstract
An unbiased method for improving the resolution of astronomical images is presented. The strategy at the core of this method is to establish a linear transformation between the recorded image and an improved image at some desirable resolution. In order to establish this transformation only the actual point spread function and a desired point spread function need be known. Any image actually recorded is not used in establishing the linear transformation between the recorded and improved image. This method has a number of advantages over other methods currently in use. It is not iterative which means it is not necessary to impose any criteria, objective or otherwise, to stop the iterations. The method does not require an artificial separation of the image into ``smooth'' and ``point-like'' components, and thus is unbiased with respect to the character of structures present in the image. The method produces a linear transformation between the recorded image and the deconvolved image and therefore the propagation of pixel-by-pixel flux error estimates into the deconvolved image is trivial. It is explicitly constrained to preserve photometry.

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