Adaptation in a class of linear inverse problems
arXiv:1310.7149
Abstract
We consider the linear inverse problem of estimating an unknown signal from noisy measurements on where the linear operator 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 varies over a wide range of Besov function classes.
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