  We investigate data compression schemes for proposed all-sky
diffraction-limited visible/NIR sky surveys aimed at the dark energy problem.
We show that lossy square-root compression to 1 bit of noise per pixel,
followed by standard lossless compression algorithms, reduces the images to
2.5-4 bits per pixel, depending primarily upon the level of cosmic-ray
contamination of the images. Compression to this level adds noise equivalent to
<10% penalty in observing time. We derive an analytic correction to flux biases
inherent to the square-root compression scheme. Numerical tests on simple
galaxy models confirm that galaxy fluxes and shapes are measured with
systematic biases <~10^{-4} induced by the compression scheme, well below the
requirements of supernova and weak gravitational lensing dark-energy
experiments. An accompanying paper (Vanderveld 2009) bounds the shape biases
using realistic simulated images of the high-Galactic-latitude sky. The
square-root preprocessing step has advantages over simple (linear) decimation
when there are many bright objects or cosmic rays in the field, or when the
background level will vary.
