Adaptation in a class of linear inverse problems

Iain M. Johnstone; Debashis Paul

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arXiv · 1310.7149

Adaptation in a class of linear inverse problems

Iain M. Johnstone·Debashis Paul

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Abstract

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.

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Iain M. Johnstone, Debashis Paul. 2014-08-22. Adaptation in a class of linear inverse problems. https://arxiv.org/abs/1310.7149

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