Deconvolution of repeated measurements corrupted by unknown noise

TL;DR

This paper addresses the deconvolution problem with repeated measurements corrupted by unknown noise, establishing identifiability, proposing an estimator with convergence rates, and demonstrating effectiveness through simulations.

Contribution

It introduces a novel approach for deconvolution in repeated measurements without noise distribution assumptions, including an adaptive estimator and theoretical guarantees.

Findings

Estimator reaches minimax rate for compact support signals

Method effective with limited sample sizes

Establishes identifiability under minimal assumptions

Abstract

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple measurements of X perturbed independently by additive errors. Our contributions include establishing identifiability without any assumption on the noise except for coordinate independence. We propose an estimator of the density of the signal for which we provide rates of convergence, and prove that it reaches the minimax rate in the case where the support of the signal is compact. Additionally, we propose a model selection procedure for adaptive estimation. Numerical simulations demonstrate the effectiveness of our approach even with limited sample sizes.