Sparse Representation of White Gaussian Noise with Application to l_0-Norm Decoding in Noisy Compressed Sensing by Ori Shental. The abstract reads:
The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is also inferred. The results are obtained via the Replica method which stems from statistical mechanics. A direct outcome of these results is the introduction of sharp threshold for l_0-norm decoding in noisy compressed sensing, and its mean-square error for underdetermined Gaussian vector channels.
I need to think some more about this paper as this idea of noise being "compressible" must have some other implications in the multiplicative noise case....Thanks Ori for the heads-up.