Wavelet shrinkage for correlated data and inverse problems: Adaptivity results

Johnstone and Silverman (1997) described a level-dependent thresholding met hod for extracting signals from correlated noise. The thresholds were chose n to minimize a data based unbiased risk criterion. Here we show that in ce rtain asymptotic models encompassing short and long range dependence, these methods are simultaneously asymptotically minimax up to constants over a b road range of Besov classes. We indicate the extension of the methods and r esults to a class of linear inverse problems possessing a wavelet vaguelett e decomposition.