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We consider the inverse problem of in-line holography, applied tominimally-destructive imaging of cold atom clouds. Absorption imagingnear-resonance provides a simple, but destructive measurement of atom columndensity. Imaging off resonance greatly reduces heating, and sequential imagesmay be taken. Under the conditions required for off-resonant imaging, thegenerally-intractable inverse problem may be linearized. Aminimally-destructive, quantitative and high-resolution image of the atom cloudcolumn density is then retrieved from a single diffraction pattern.Comment: 4 pages, 3 figures v2: minor changes in response to referee reports,  mostly additional experimental detail v3: revisions to figure 3: added trace  and changed image. Minor text and referencing changes. Accepted by Phys Rev A  (Rapid Commun

Diffraction-contrast imaging of cold atoms