Sparse Representation of White Gaussian Noise with Application to L0-Norm Decoding in Noisy Compressed Sensing

摘要

The achievable and converse regions for sparse representation of whiteGaussian noise based on an overcomplete dictionary are derived in the limit oflarge systems. Furthermore, the marginal distribution of such sparserepresentations is also inferred. The results are obtained via the Replicamethod which stems from statistical mechanics. A direct outcome of theseresults is the introduction of sharp threshold for $\ell_{0}$-norm decoding innoisy compressed sensing, and its mean-square error for underdeterminedGaussian vector channels.