Deconvolution in white noise with a random blurring function
Thomas Willer
Abstract
We consider the problem of denoising a function observed after a convolution with a random filter independent of the noise and satisfying some mean smoothness condition depending on an ill posedness coefficient. We establish the minimax rates for the Lp risk over balls of periodic Besov spaces with respect to the level of noise, and we provide an adaptive estimator achieving these rates up to log factors. Simulations were performed to highlight the effects of the ill posedness and of the distribution of the filter on the efficiency of the estimator.
Create a lesson
Related papers
Instance-Optimal Adaptive Location Estimation via Multiscale Mid-Summaries
Qiaosen Wang, Chao Gao
Robust Multi-Task Learning for Principal Component Analysis
Dali Liu, Haolei Weng
Principal component error in high-dimensional factor models
Alex Bernstein, Lisa R. Goldberg, Nicholas Gunther et al.
Approximation Theorems for High-Dimensional Canonical U-Statistics: Gaussian Chaos and Phase Transition
Leheng Cai, Qirui Hu
On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes
Jean-Pierre Delmas, Habti Abeida, Stefano Fortunati
Inference for two-stage sampling in spatial surveys
Guillaume Chauvet, Olivier Bouriaud, Trinh H. K. Duong