Reduction Of Correlated Noise Using A Library Of Orthonormal Bases

. We study the application of a library of orthonormal bases to the reduction of correlated Gaussian noise. A joint condition on the library and the noise covariance is derived which ensures that simple thresholding in an adaptively chosen basis yields an estimation error within a logarithmic factor of the ideal risk. In the model example of a wavelet packet library and stationary noise the condition can be translated into a reverse Holder inequality on the power spectrum. 1. Introduction Consider signals given as vectors in R N , and assume that a finite library L of orthonormal bases is available. The total collection of w 2 B, B 2 L defines a dictionary D of M vectors. If L consists of only one basis, we have M = N . In general M NjLj where jLj is the number of bases in L. For the examples we have in mind, however, it holds that M NjLj. For wavelet packet libraries one has M = N(1 + log 2 N) while jLj ? 1:5 N , [CW]. Let a clean signal s be corrupted by additive noise z so t..