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Contributions à la microscopie à fluorescence en imagerie biologique : modélisation de la PSF, restauration d'images et détection super-résolutive

Abstract : This thesis mainly contributes to three aspects in fluorescence microscopy imaging. (i) Optical system modeling: we have comprehensively studied the least squares Gaussian approximations of the diffraction-limited 2D/3D paraxial/non-paraxial point spread functions (PSFs) of wide-field fluorescence microscope (WFFM), laser-scanning confocal microscope (LSCM) and disk-scanning confocal microscope (DSCM) described using the Debye diffraction integrals. Optimal Gaussian parameters are derived for the 2D paraxial WFFM PSF, under both the Linf and L1 normalizations. For the other PSFs, with the Linf normalization, near-optimal parameters in explicit forms are derived using Maclaurin series matching. These Gaussian approximative PSF models allow fast computation and greatly simplify the modeling of biological objects under these microscopes. (ii) Fluorescence image denoising: images produced by LSCM and DSCM have either a Poisson or a mixed-Poisson-Gaussian (MPG) statistical nature according to different function modes of the microscope. We have proposed two approaches for Poisson noise removal. One method is based on biorthogonal Haar-domain hypothesis tests, which is particularly suitable for fast estimating smooth intensities from large datasets. Our second method makes use of a well designed variance stabilizing transform (VST) allowing to Gaussianize and stabilize a filtered Poisson process. This VST can be combined with most multi-scale transforms yielding multi-scale VSTs (MS-VST). We show that this MS-VST approach provides a very effective denoiser capable of recovering important structures of various (isotropic, line-like and curvilinear) shapes in (very) low-count images. This MS-VST method has also been extended to remove MPG noise, and to extract fluorescent spots within MPG noisy data. (iii) Super-resolution object detection: we have reviewed and extended the results of resolution limits for point-like sources under detection-theoretic, estimation-theoretic and information-theoretic points of view. In particular, we propose to apply the VST to study the limiting resolution with Poisson or MPG data, leading to asymptotically consistent results with closed-form expressions. We have also generalized an existing super-resolution approach, which is based on parametric model fitting and model-order selection, to localize an unknown number of spots or rods. This method allows not only to localize sources having complex spatial configurations, but also to detect objects separated with distances smaller than Rayleigh optical resolution (super-resolution).
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Contributor : Ecole Télécom Paristech <>
Submitted on : Friday, January 11, 2008 - 8:00:00 AM
Last modification on : Friday, July 31, 2020 - 10:44:07 AM
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  • HAL Id : pastel-00003273, version 1


Bo Zhang. Contributions à la microscopie à fluorescence en imagerie biologique : modélisation de la PSF, restauration d'images et détection super-résolutive. Mathématiques [math]. Télécom ParisTech, 2007. Français. ⟨pastel-00003273⟩



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