Deconvolution of repeated measurements corrupted by unknown noise

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.