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Multiview Attenuation Estimation and Correction

  • Valentin DebarnotEmail author
  • Jonas Kahn
  • Pierre Weiss
Article
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Abstract

Measuring attenuation coefficients is a fundamental problem that can be solved with diverse techniques such as X-ray or optical tomography and lidar. We propose a novel approach based on the observation of a sample from a few different angles. This principle can be used in existing devices such as lidar or various types of fluorescence microscopes. It is based on the resolution of a nonlinear inverse problem. We propose a specific computational approach to solve it and show the well-foundedness of the approach on simulated data. Some of the tools developed are of independent interest. In particular, we propose an efficient method to correct attenuation defects, new robust solvers for the lidar equation as well as new efficient algorithms to compute the proximal operator of the logsumexp function in dimension 2.

Keywords

Nonconvex optimization Bayesian estimation Lidar Fluorescence microscopy Multiview estimation Poisson noise 

Notes

Acknowledgements

This work was supported by the Fondation pour la Recherche Médicale (FRM Grant Number ECO20170637521 to V.D.) and by Plan CANCER, MIMMOSA project. The authors wish to thank Juan Cuesta, Emilio Gualda, Jan Huisken, Philipp Keller, Théo Liu, Jürgen Mayer and Anne Sentenac for interesting discussions and feedbacks on the model. They thank the anonymous reviewers for pointing out reference [30], which is closely related to this paper.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ITAV, CNRSToulouseFrance
  2. 2.IMT and ITAVCNRS and Université de ToulouseToulouseFrance

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