Minimax adaptive wavelet estimator for the simultaneous blind deconvolution with fractional Gaussian noise

TL;DR

This paper introduces an adaptive wavelet estimator for simultaneous blind deconvolution under fractional Gaussian noise, achieving near-optimal convergence rates across various Besov spaces by considering dependence and noise sources.

Contribution

The paper develops a minimax adaptive wavelet estimator that effectively handles multiple channels with dependence and noise, providing near-optimal convergence rates.

Findings

Estimator attains minimax near-optimal rates in Besov spaces

Convergence rates depend on the weakest channel dependence

Method accounts for both noise sources in deconvolution

Abstract

We construct an adaptive wavelet estimator that attains minimax near-optimal rates in a wide range of Besov balls. The convergence rates are affected only by the weakest dependence amongst the channels, and take into account both noise sources.