Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems

02/01/2020
by   Abhishake Rastogi, et al.
0

In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/24/2020

Inverse learning in Hilbert scales

We study the linear ill-posed inverse problem with noisy data in the sta...
research
02/14/2019

Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems

We study a non-linear statistical inverse learning problem, where we obs...
research
08/28/2022

Statistical Inverse Problems in Hilbert Scales

In this paper, we study the Tikhonov regularization scheme in Hilbert sc...
research
01/02/2020

Regularization of Inverse Problems

These lecture notes for a graduate class present the regularization theo...
research
11/22/2022

Least squares approximations in linear statistical inverse learning problems

Statistical inverse learning aims at recovering an unknown function f fr...
research
04/29/2020

A novel two-point gradient method for Regularization of inverse problems in Banach spaces

In this paper, we introduce a novel two-point gradient method for solvin...
research
04/16/2022

PAC-Bayesian Based Adaptation for Regularized Learning

In this paper, we propose a PAC-Bayesian a posteriori parameter selectio...

Please sign up or login with your details

Forgot password? Click here to reset