Ideal denoising for signals in sub-Gaussian noise

Donoho and Johnstone introduced an algorithm and supporting inequality that allows the selection of an orthonormal basis for optimal denoising. The present paper concentrates in extending and improving this result, the main contribution is to incorporate a wider class of noise vectors. The class of strict sub-Gaussian random vectors allow us to obtain large deviation inequalities in a uniform way over all basis in a given library. The results are obtained maintaining the algorithmic properties of the original results.