# Une approche problèmes inverses pour la reconstruction de données multi-dimensionnelles par méthodes d'optimisation.

Abstract : This work presents an inverse problems'' approach for reconstruction in two different fields: digital holography and blind deconvolution.
The "inverse problems" approach consists in investigating the causes from their effects, i.e. estimate the parameters describing a system from its observation. In general, same causes produce same effects, same effects can however have different causes. To remove ambiguities, it is necessary to introduce a priori information. In this work, the parameters are estimated using optimization methods to minimize a cost function which consists of a likelihood term plus some prior terms.

We use this approach to address the problem of heterogeneous multidimensional data blind deconvolution. Heterogeneous means that the different dimensions have different meanings and units (for instance position and wavelength). For that, we have established a general framework with a separable prior which have been successfully adapted to different applications: deconvolution of multi-spectral data in astronomy, of Bayer color images and blind deconvolution of bio-medical video sequences (in coronarography, conventional and confocal microscopy).

We also applied this framework to digital holography for particles image velocimetry (DH-PIV). Using a model of the hologram formation, we use this "inverse problems" approach to circumvent the artifacts produced by the classical hologram restitution methods (distortions close to the image boundaries, multiple focusing, twin-images). The proposed algorithm detects micro-particles in a volume 16 times larger than the camera field of view and with a precision improved by a factor 5 compared with classical techniques.
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https://tel.archives-ouvertes.fr/tel-00379735
Contributor : Ferréol Soulez <>
Submitted on : Tuesday, April 27, 2010 - 3:33:32 PM
Last modification on : Friday, April 5, 2019 - 8:04:56 PM
Long-term archiving on : Wednesday, November 30, 2016 - 5:17:38 PM

### Identifiers

• HAL Id : tel-00379735, version 2

### Citation

Ferréol Soulez. Une approche problèmes inverses pour la reconstruction de données multi-dimensionnelles par méthodes d'optimisation.. Traitement du signal et de l'image [eess.SP]. Université Jean Monnet - Saint-Etienne, 2008. Français. ⟨tel-00379735v2⟩

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