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On accuracy and existence of approximate decoders for ill-posed inverse problems

Gottschling, Nina Maria and Campodonico, Paolo and Antun, Vegard and Hansen, Anders C. (2023) On accuracy and existence of approximate decoders for ill-posed inverse problems. International Symposium on Computational Sensing, 2023, 12-14 Jun 2023, Luxembourg.

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Based on work by Cohen, Damen and Devore \and Bourrier et. al., we propose a framework that highlights the importance of knowing the measurement model $F$ and model class $\mathcal{M}_1$, for solving ill-posed (non-)linear inverse problems. Previous work has assumed that the measurement model is injective on the model class $\mathcal{M}_1$ and we obviate the need for this assumption. We establish fundamental upper and lower bounds on the reconstruction accuracy of an inverse problem in terms of the kernel size. The key definition introduced in this work, the kernel size of an inverse problem, only requires the measurement model $F$ and model class $\mathcal{M}_1$ to be computed. Thus, it is applicable in deep learning (DL) based settings where $\mathcal{M}_1$ can be an arbitrary data set.

Item URL in elib:https://elib.dlr.de/195729/
Document Type:Conference or Workshop Item (Poster)
Title:On accuracy and existence of approximate decoders for ill-posed inverse problems
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Campodonico, PaoloUniversity of Cambridge, UKUNSPECIFIEDUNSPECIFIED
Antun, VegardUniversity of Oslo, NorwayUNSPECIFIEDUNSPECIFIED
Hansen, Anders C.University of Cambridge, UKUNSPECIFIEDUNSPECIFIED
Date:13 June 2023
Refereed publication:No
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Keywords:Inverse problems, Deep Learning, Approximation Theory
Event Title:International Symposium on Computational Sensing, 2023
Event Location:Luxembourg
Event Type:international Conference
Event Dates:12-14 Jun 2023
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Earth Observation
DLR - Research area:Raumfahrt
DLR - Program:R EO - Earth Observation
DLR - Research theme (Project):R - Artificial Intelligence
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Atmospheric Physics > Earth System Modelling
Deposited By: Gottschling, Nina Maria
Deposited On:06 Jul 2023 09:28
Last Modified:06 Jul 2023 09:28

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