# Variational regularisation for inverse problems with imperfect forward operators and general noise models

arXiv: https://arxiv.org/abs/2005.14131 · HTML: https://mlsanity.com/paper/2005.14131/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2020.

## Built on by (most cited first, 6 of 6)

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- [Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem](https://mlsanity.com/paper/2207.01466/) (2022)
- [Model-corrected learned primal-dual models for fast limited-view photoacoustic tomography](https://mlsanity.com/paper/2304.01963/) (2023)
- [Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise](https://mlsanity.com/paper/2108.03642/) (2021)
- [An Adaptively Inexact Method for Bilevel Learning Using Primal-Dual Style Differentiation](https://mlsanity.com/paper/2412.06436/) (2024)

## Abstract (arXiv)

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals. Both for a-priori and a-posteriori parameter choice rules, we obtain convergence rates of the regularized solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, f-divergences, norms, as well as sums and infimal convolutions of those.