  In this paper we propose a new framework for distributed source coding of
structured sources, such as sparse signals. Our framework capitalizes on recent
advances in the theory of linear inverse problems and signal representations
using incoherent projections. Our approach acquires and quantizes incoherent
linear measurements of the signal, which are represented as separate bitplanes.
Each bitplane is coded using a distributed source code of the appropriate rate,
and transmitted. The decoder, starts from the least significant biplane and,
using a prediction of the signal as side information, iteratively recovers each
bitplane based on the source prediction and the signal, assuming all the
previous bitplanes of lower significance have already been recovered. We
provide theoretical results guiding the rate selection, relying only on the
least squares prediction error of the source. This is in contrast to existing
approaches which rely on difficult-to-estimate information-theoretic metrics to
set the rate. We validate our approach using simulations on remote-sensing
multispectral images, comparing them with existing approaches of similar
complexity.
