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We have developed a method for the linear reconstruction of an image fromundersampled, dithered data, which has been used to create the distributed,combined Hubble Deep Field images -- the deepest optical images yet taken ofthe universe. The algorithm, known as Variable-Pixel Linear Reconstruction (orinformally as "drizzling"), preserves photometry and resolution, can weightinput images according to the statistical significance of each pixel, andremoves the effects of geometric distortion both on image shape and photometry.In this paper, the algorithm and its implementation are described, andmeasurements of the photometric accuracy and image fidelity are presented. Inaddition, we describe the use of drizzling to combine dithered images in thepresence of cosmic rays.Comment: Invited paper, to appear in Applications of Digital Image Processing  XX, ed. A. Tescher, Proc. S.P.I.E. vol. 3164, in press; 6 pages, 4 included  figures, SPIE LaTex style file include

<title>Novel image-reconstruction method applied to deep Hubble space telescope images</title>