  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.
