Adaptation in a class of linear inverse problems

2013/10/26 by Iain M. Johnstone, Debashis Paul, Johnstone, Iain M. +1
Computer Science · Engineering · Mathematics · #62C20 #62G08 #FOS: Mathematics #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62C20 #msc:62G08 #stat.TH

paper · pdf · doi:10.48550/arxiv.1310.7149

3 figures

openalex publication_date 2013/10/26 · arxiv created 2014/08/22 · arxiv updated 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Adapting to unknown sparsity by controlling the false discovery rate

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