Wavelet shrinkage with correlated wavelet coefficients

This paper investigates the statistical characterizationof mul-tiscale wavelet coefficients corresponding to random signals and images. Virtually all approaches to wavelet shrinkage model the wavelet coefficients as independent; we challenge that assumption and demonstrate several cases where sub-stantial correlations may be present in the wavelet domain. In particular, the correlation between scales can be surpris-ingly substantial, even for pixels separated by several scales. Our goal, initiated in this paper, is to develop an efficient random field model describing these statistical correlations, and demonstrate its effectiveness in the context of Bayesian wavelet shrinkage for signal and image denoising. 1