  We consider the linear inverse problem of estimating an unknown signal $f$
from noisy measurements on $Kf$ where the linear operator $K$ admits a
wavelet-vaguelette decomposition (WVD). We formulate the problem in the
Gaussian sequence model and propose estimation based on complexity penalized
regression on a level-by-level basis. We adopt squared error loss and show that
the estimator achieves exact rate-adaptive optimality as $f$ varies over a wide
range of Besov function classes.
