Inverse problems with second-order Total Generalized Variation constraints

05/19/2020
by   Kristian Bredies, et al.
0

Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to the k-th distributional derivative and leads to desirable results when applied to image denoising, i.e., L^2-fitting with TGV penalty. The present paper studies TGV of second order in the context of solving ill-posed linear inverse problems. Existence and stability for solutions of Tikhonov-functional minimization with respect to the data is shown and applied to the problem of recovering an image from blurred and noisy data.

READ FULL TEXT

page 2

page 4

research
01/09/2020

A note on the minimization of a Tikhonov functional with ℓ^1-penalty

In this paper, we consider the minimization of a Tikhonov functional wit...
research
06/11/2018

Statistics on functional data and covariance operators in linear inverse problems

We introduce a framework for the statistical analysis of functional data...
research
11/24/2022

To be or not to be stable, that is the question: understanding neural networks for inverse problems

The solution of linear inverse problems arising, for example, in signal ...
research
10/07/2021

On the asymptotical regularization with convex constraints for inverse problems

In this paper, we consider the asymptotical regularization with convex c...
research
09/23/2022

A Second-Order TGV Discretization with Some Invariance Properties

In this work, we propose a new discretization for second-order total gen...
research
09/24/2020

Alternating minimization for a single step TV-Stokes model for image denoising

The paper presents a fully coupled TV-Stokes model, and propose an algor...
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...

Please sign up or login with your details

Forgot password? Click here to reset