Multiview Attenuation Estimation and Correction

Valentin Debarnot (1) , Jonas Kahn (1, 2) , Pierre Weiss (1, 2)

1 ITAV - Institut des Technologies Avancées en sciences du Vivant
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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 Lambert W function and the proximal operator of the logsumexp function in dimension 2.

Mots clés: Attenuation Correction; Attenuation coefficient; Nonlinear inverse problems; Convex optimization; Nonconvex and nonsmooth optimization; Special functions

Domaines: Traitement du signal et de l'image [eess.SP]; Imagerie; Optimisation et contrôle [math.OC]

Valentin Debarnot, Jonas Kahn, Pierre Weiss. Multiview Attenuation Estimation and Correction. Journal of Mathematical Imaging and Vision, 2019, pp.1-18. ⟨10.1007/s10851-019-00871-6⟩. ⟨hal-01429148⟩