On Learned Operator Correction in Inverse Problems

Lunz, Sebastian; Hauptmann, Andreas; Tarvainen, Tanja; Schönlieb, Carola‐Bibiane; Arridge, Simon

doi:10.48550/arxiv.2005.07069

Cited by 2 publications

(2 citation statements)

References 40 publications

(99 reference statements)

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“…Explicit corrections, as we investigate here, have been recently analyzed in [17], where the authors show that under sufficient approximation accuracy, we can expect to obtain solutions close to what we obtain with a correct model. We will take this as motivation and shall take the step to more demanding nonlinear inverse problems and verify the proposed techniques to experimental data.…”

Section: Introductionsupporting

confidence: 56%

Learning and correcting non-Gaussian model errors

Smyl

Tallman

Black

et al. 2021

Journal of Computational Physics

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All discretized numerical models contain modelling errors -this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves quantitative results from frameworks using numerical models in prediction, tomography, and signal processing. Further to this, the compensation of highly nonlinear and non-Gaussian modelling errors, arising in many ill-conditioned systems aiming to capture complex physics, is a historically difficult task. In this work, we address this challenge by proposing a neural network approach capable of accurately approximating and compensating for such modelling errors in augmented direct and inverse problems. The viability of the approach is demonstrated using simulated and experimental data arising from differing physical direct and inverse problems.

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Section: Introductionsupporting

confidence: 56%

Learning and correcting non-Gaussian model errors

Smyl

Tallman

Black

et al. 2021

Journal of Computational Physics

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“…This is possibly because CNNs can learn and compensate non-Gaussian modelling errors more efficiently than BAE, which assumes modelling errors as Gaussian. The authors refer to [43] for more discussions on modelling error corrections using CNNs.…”

Section: Discussionmentioning

confidence: 99%

A model-based iterative learning approach for diffuse optical tomography

Mozumder¹,

Hauptmann²,

Nissilä³

et al. 2021

Preprint

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Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning techniques, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the absorption and scattering coefficients utilising a 'modelbased' learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.

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On Learned Operator Correction in Inverse Problems

Cited by 2 publications

References 40 publications

Learning and correcting non-Gaussian model errors

Learning and correcting non-Gaussian model errors

A model-based iterative learning approach for diffuse optical tomography

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