  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.

Instrumentation and Methods for Astrophysics