Publications de Z. Kam

Résultat de la recherche dans la liste des publications :

• 2 Articles
• 7 Articles de conférence
• 3 Rapports de recherche et Rapports techniques

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2 Articles

1 - Blind deconvoltion for thin layered confocal imaging. P. Pankajakshan et B. Zhang et L. Blanc-Féraud et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Applied Optics, 48(22): pages 4437-4448, août 2009. Mots-clés : Blind Deconvolution, Microscopie confocale, Problèmes Inverses. Copyright : Optical Society of America @ARTICLE{ppankajakshan09b, author = {Pankajakshan, P. and Zhang, B. and Blanc-Féraud, L. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {Blind deconvoltion for thin layered confocal imaging}, year = {2009}, month = {août}, journal = {Applied Optics}, volume = {48}, number = {22}, pages = {4437-4448}, pdf = {http://hal.inria.fr/docs/00/39/55/23/PDF/AppliedOpticsPaperTypesetting.pdf}, keyword = {Blind Deconvolution, Microscopie confocale, Problèmes Inverses} } Abstract : We propose an alternate minimization algorithm for estimating the point-spread function (PSF) of a confocal laser scanning microscope and the specimen fluorescence distribution. A three-dimensional separable Gaussian model is used to restrict the PSF solution space and a constraint on the specimen is used so as to favor the stabilization and convergence of the algorithm. The results obtained from the simulation show that the PSF can be estimated to a high degree of accuracy, and those on real data show better deconvolution as compared to a full theoretical PSF model.

2 - Richardson-Lucy Algorithm with Total Variation Regularization for 3D Confocal Microscope Deconvolution. N. Dey et L. Blanc-Féraud et C. Zimmer et Z. Kam et P. Roux et J.C. Olivo-Marin et J. Zerubia. Microscopy Research Technique, 69: pages 260-266, avril 2006. Mots-clés : Microscopie confocale, Methodes variationnelles, Variation totale, Deconvolution. @ARTICLE{dey_mrt_05, author = {Dey, N. and Blanc-Féraud, L. and Zimmer, C. and Kam, Z. and Roux, P. and Olivo-Marin, J.C. and Zerubia, J.}, title = {Richardson-Lucy Algorithm with Total Variation Regularization for 3D Confocal Microscope Deconvolution}, year = {2006}, month = {avril}, journal = {Microscopy Research Technique}, volume = {69}, pages = {260-266}, url = {http://dx.doi.org/10.1002/jemt.20294}, keyword = {Microscopie confocale, Methodes variationnelles, Variation totale, Deconvolution} } Abstract : Confocal laser scanning microscopy is a powerful and popular technique for 3D imaging of biological specimens. Although confocal microscopy images are much sharper than standard epifluorescence ones, they are still degraded by residual out-of-focus light and by Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes a maximum likelihood estimation adapted to Poisson statistics. As this algorithm tends to amplify noise, regularization constraints based on some prior knowledge on the data have to be applied to stabilize the solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularization constraint based on Total Variation, which suppresses unstable oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results as compared to the unregularized Richardson-Lucy algorithm, both visually and quantitatively.

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7 Articles de conférence

1 - Wavefront sensing for aberration modeling in fluorescence MACROscopy. P. Pankajakshan et A. Dieterlen et G. Engler et Z. Kam et L. Blanc-Féraud et J. Zerubia et J.C. Olivo-Marin. Dans Proc. IEEE International Symposium on Biomedical Imaging (ISBI), Chicago, USA, avril 2011. Mots-clés : fluorescence MACROscopy , phase retrieval, field aberration. @INPROCEEDINGS{PanjakshanISBI2011, author = {Pankajakshan, P. and Dieterlen, A. and Engler, G. and Kam, Z. and Blanc-Féraud, L. and Zerubia, J. and Olivo-Marin, J.C.}, title = {Wavefront sensing for aberration modeling in fluorescence MACROscopy}, year = {2011}, month = {avril}, booktitle = {Proc. IEEE International Symposium on Biomedical Imaging (ISBI)}, address = {Chicago, USA}, url = {http://hal.inria.fr/inria-00563988/en/}, keyword = {fluorescence MACROscopy , phase retrieval, field aberration} } Abstract : In this paper, we present an approach to calculate the wavefront in the back pupil plane of an objective in a fluorescent MACROscope. We use the three-dimensional image of a fluorescent bead because it contains potential pupil information in the ‘far’ out-of-focus planes for sensing the wavefront at the back focal plane of the objective. Wavefront sensing by phase retrieval technique is needed for several reasons. Firstly, the point-spread function of the imaging system can be calculated from the estimated pupil phase and used for image restoration. Secondly, the aberrations in the optics of the objective can be determined by studying this phase. Finally, the estimated wavefront can be used to correct the aberrated optical path with- out a wavefront sensor. In this paper, we estimate the wavefront of a MACROscope optical system by using Bayesian inferencing and derive the Gerchberg-Saxton algorithm as a special case.

2 - Point-spread function model for fluorescence MACROscopy imaging. P. Pankajakshan et Z. Kam et A. Dieterlen et G. Engler et L. Blanc-Féraud et J. Zerubia et J.C. Olivo-Marin. Dans Asilomar Conference on Signals, Systems and Computers, pages 1364-136, Pacific Grove, CA, USA , novembre 2010. Mots-clés : fluorescence MACROscopy , point-spread function, pupil function, vignetting . @INPROCEEDINGS{PanjakshanASILOMAR2010, author = {Pankajakshan, P. and Kam, Z. and Dieterlen, A. and Engler, G. and Blanc-Féraud, L. and Zerubia, J. and Olivo-Marin, J.C.}, title = {Point-spread function model for fluorescence MACROscopy imaging}, year = {2010}, month = {novembre}, booktitle = {Asilomar Conference on Signals, Systems and Computers}, pages = {1364-136}, address = {Pacific Grove, CA, USA }, url = {http://hal.inria.fr/inria-00555940/}, keyword = {fluorescence MACROscopy , point-spread function, pupil function, vignetting } } Abstract : In this paper, we model the point-spread function (PSF) of a fluorescence MACROscope with a field aberration. The MACROscope is an imaging arrangement that is designed to directly study small and large specimen preparations without physically sectioning them. However, due to the different optical components of the MACROscope, it cannot achieve the condition of lateral spatial invariance for all magnifications. For example, under low zoom settings, this field aberration becomes prominent, the PSF varies in the lateral field, and is proportional to the distance from the center of the field. On the other hand, for larger zooms, these aberrations become gradually absent. A computational approach to correct this aberration often relies on an accurate knowledge of the PSF. The PSF can be defined either theoretically using a scalar diffraction model or empirically by acquiring a three-dimensional image of a fluorescent bead that approximates a point source. The experimental PSF is difficult to obtain and can change with slight deviations from the physical conditions. In this paper, we model the PSF using the scalar diffraction approach, and the pupil function is modeled by chopping it. By comparing our modeled PSF with an experimentally obtained PSF, we validate our hypothesis that the spatial variance is caused by two limiting optical apertures brought together on different conjugate planes.

3 - Point-spread function retrieval for fluorescence microscopy. P. Pankajakshan et L. Blanc-Féraud et Z. Kam et J. Zerubia. Dans Proc. IEEE International Symposium on Biomedical Imaging (ISBI), Publ. IEEE, Org. IEEE, Boston, USA, juin 2009. Mots-clés : fluorescence microscopy, point spread function, Algorithme EM, Deconvolution. Copyright : Copyright 2009 IEEE. Published in the 2009 International Symposium on Biomedical Imaging: From Nano to Macro (ISBI 2009), scheduled for June 28 - July 1, 2009 in Boston, Massachusetts, U.S.A. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works, must be obtained from the IEEE. Contact: Manager, Copyrights and Permissions / IEEE Service Center / 445 Hoes Lane / P.O. Box 1331 / Piscataway, NJ 08855-1331, USA. Telephone: + Intl. 908-562-3966. @INPROCEEDINGS{ppankajakshan09a, author = {Pankajakshan, P. and Blanc-Féraud, L. and Kam, Z. and Zerubia, J.}, title = {Point-spread function retrieval for fluorescence microscopy}, year = {2009}, month = {juin}, booktitle = {Proc. IEEE International Symposium on Biomedical Imaging (ISBI)}, publisher = {IEEE}, organization = {IEEE}, address = {Boston, USA}, pdf = {http://hal.inria.fr/docs/00/39/55/34/PDF/pankajakshan.pdf}, keyword = {fluorescence microscopy, point spread function, Algorithme EM, Deconvolution} } Abstract : In this paper we propose a method for retrieving the Point-Spread Function (PSF) of an imaging system given the observed images of fluorescent microspheres. Theoretically calculated PSFs often lack the experimental or microscope specific signatures while empirically obtained data are either over sized or (and) too noisy. The effect of noise and the influence of the microsphere size can be mitigated from the experimental data by using a Maximum Likelihood Expectation Maximization (MLEM) algorithm. The true experimental parameters can then be estimated by fitting the result to a model based on the scalar diffraction theory. The algorithm was tested on some simulated data and the results obtained validate the usefulness of the approach for retrieving the PSF from measured data.

4 - Blind deconvolution for diffraction-limited fluorescence microscopy. P. Pankajakshan et B. Zhang et L. Blanc-Féraud et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Dans Proc. IEEE International Symposium on Biomedical Imaging (ISBI), pages 740-743, Paris, France, mai 2008. Mots-clés : Microscopie confocale, Blind Deconvolution, point spread function, Richardson-Lucy algorithm, total variation regularization. Copyright : This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. @INPROCEEDINGS{ppankajakshan08a, author = {Pankajakshan, P. and Zhang, B. and Blanc-Féraud, L. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {Blind deconvolution for diffraction-limited fluorescence microscopy}, year = {2008}, month = {mai}, booktitle = {Proc. IEEE International Symposium on Biomedical Imaging (ISBI)}, pages = {740-743}, address = {Paris, France}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2008_ppankajakshan08a.pdf}, keyword = {Microscopie confocale, Blind Deconvolution, point spread function, Richardson-Lucy algorithm, total variation regularization} } Abstract : Optical Sections of biological samples obtained from a fluorescence Confocal Laser Scanning Microscopes (CLSM) are often degraded by out-of-focus blur and photon counting noise. Such physical constraints on the observation are a result of the diffraction-limited nature of the optical system, and the reduced amount of light detected by the photomultiplier respectively. Hence, the image stacks can benefit from postprocessing restoration methods based on deconvolution. The parameters of the acquisition system’s Point Spread Function (PSF) may vary during the course of experimentation, and so they have to be estimated directly from the observation data. We describe here an alternate minimization algorithm for the simultaneous blind estimation of the specimen 3D distribution of fluorescent sources and the PSF. Experimental results on real data show that the algorithm provides very good deconvolution results in comparison to theoretical microscope PSF models.

5 - Parametric blind deconvolution for confocal laser scanning microscopy. P. Pankajakshan et B. Zhang et L. Blanc-Féraud et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Dans Proc. 29th International Conference of IEEE EMBS (EMBC-07), pages 6531-6534, août 2007. Mots-clés : Microscopie confocale, Blind Deconvolution, Poisson noise, Variation totale, Algorithme EM, Estimation bayesienne. Copyright : ©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. @INPROCEEDINGS{Pankajakshan07a, author = {Pankajakshan, P. and Zhang, B. and Blanc-Féraud, L. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {Parametric blind deconvolution for confocal laser scanning microscopy}, year = {2007}, month = {août}, booktitle = {Proc. 29th International Conference of IEEE EMBS (EMBC-07)}, pages = {6531-6534}, pdf = {http://ieeexplore.ieee.org/iel5/4352184/4352185/04353856.pdf?tp=&isnumber=&arnumber=4353856}, keyword = {Microscopie confocale, Blind Deconvolution, Poisson noise, Variation totale, Algorithme EM, Estimation bayesienne} } Abstract : In this paper, we propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscopic (CLSM) images and parametric estimation of the acquisition system’s Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the images suffers from two basic physical limitations. The diffraction-limited nature of the optical system, and the reduced amount of light detected by the photomultiplier cause blur and photon counting noise respectively. These images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observed data. A priori model of the specimen is further applied to stabilize the alternate minimization algorithm and to converge to the solutions.

6 - Deconvolution in confocal microscopy with total variation regularization. N. Dey et L. Blanc-Féraud et C. Zimmer et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Dans Proc. French-Danish Workshop on Spatial Statistics and Image Analysis in Biology (SSIAB), pages 117--120, mai 2004. @INPROCEEDINGS{Dey04b, author = {Dey, N. and Blanc-Féraud, L. and Zimmer, C. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {Deconvolution in confocal microscopy with total variation regularization}, year = {2004}, month = {mai}, booktitle = {Proc. French-Danish Workshop on Spatial Statistics and Image Analysis in Biology (SSIAB)}, pages = {117--120}, url = {http://www3.jouy.inra.fr/miaj/public/imaste/ssiab2004/program/abw92/}, keyword = {} }

7 - A deconvolution method for confocal microscopy with total variation regularization. N. Dey et L. Blanc-Féraud et C. Zimmer et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Dans Proc. IEEE International Symposium on Biomedical Imaging (ISBI), Arlington, USA, avril 2004. Mots-clés : 3D confocal microscopy, Poisson deconvolution, total variation regularization. @INPROCEEDINGS{Dey04a, author = {Dey, N. and Blanc-Féraud, L. and Zimmer, C. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {A deconvolution method for confocal microscopy with total variation regularization}, year = {2004}, month = {avril}, booktitle = {Proc. IEEE International Symposium on Biomedical Imaging (ISBI)}, address = {Arlington, USA}, pdf = {http://dx.doi.org/10.1109/ISBI.2004.1398765}, keyword = {3D confocal microscopy, Poisson deconvolution, total variation regularization} } Abstract : Confocal laser scanning microscopy is a powerful and increasingly popular technique for 3D imaging of biological specimens. However the acquired images are degraded by blur from out-of-focus light and Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy algorithm, which computes a maximum likelihood estimation adapted to Poisson statistics. However this method tends to amplify noise if used without regularizing constraint. Here, we propose to combine the Richardson-Lucy algorithm with a regularizing constraint based on total variation, whose smoothing avoids oscillations while preserving edges. We show on simulated images that this constraint improves the deconvolution result both visually and using quantitative measures.

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3 Rapports de recherche et Rapports techniques

1 - Space non-invariant point-spread function and its estimation in fluorescence microscopy. P. Pankajakshan et L. Blanc-Féraud et Z. Kam et J. Zerubia. Research Report 7157, INRIA, décembre 2009. Mots-clés : Confocal Laser Scanning Microscopy, point spread function, Estimation bayesienne, Estimation MAP, Deconvolution, fluorescence microscopy. @TECHREPORT{ppankajakshan09c, author = {Pankajakshan, P. and Blanc-Féraud, L. and Kam, Z. and Zerubia, J.}, title = {Space non-invariant point-spread function and its estimation in fluorescence microscopy}, year = {2009}, month = {décembre}, institution = {INRIA}, type = {Research Report}, number = {7157}, url = {http://hal.archives-ouvertes.fr/inria-00438719/en/}, keyword = {Confocal Laser Scanning Microscopy, point spread function, Estimation bayesienne, Estimation MAP, Deconvolution, fluorescence microscopy} } Résumé : Dans ce rapport de recherche, nous rappelons brièvement comment la nature limitée de diffraction de l'objectif d'un microscope optique, et le bruit intrinsèque peuvent affecter la résolution d'une image observée. Un algorithme de déconvolution aveugle a été proposé en vue de restaurer les fréquences manquants au delà de la limite de diffraction. Cependant, sous d'autres conditions, l'approximation du systéme imageur l'imagerie sans aberration n'est plus valide et donc les aberrations de la phase du front d'onde émergeant d'un médium ne sont plus ignorées. Dans la deuxième partie de ce rapport de recherche, nous montrons que la distribution d'intensité originelle et la localisation d'un objet peuvent être retrouvées uniquement en obtenant de la phase du front d'onde réfracté, à partir d'images d'intensité observées. Nous démontrons cela par obtention de la fonction de ou a partir d'une microsphère imagée. Le bruit et l'influence de la taille de la microsphère peuvent être diminués et parfois complètement supprimes des images observées en utilisant un estimateur maximum a posteriori. Néanmoins, a cause de l'incohérence du système d'acquisition, une récupération de phase a partir d'intensités observées n'est possible que si la restauration de la phase est contrainte. Nous avons utilisé l'optique géométrique pour modéliser la phase du front d'onde réfracté, et nous avons teste l'algorithme sur des images simulées. Abstract : In this research report, we recall briefly how the diffraction-limited nature of an optical microscope's objective, and the intrinsic noise can affect the observed images' resolution. A blind deconvolution algorithm can restore the lost frequencies beyond the diffraction limit. However, under other imaging conditions, the approximation of aberration-free imaging, is not applicable, and the phase aberrations of the emerging wavefront from a specimen immersion medium cannot be ignored any more. We show that an object's location and its original intensity distribution can be recovered by retrieving the refracted wavefront's phase from the observed intensity images. We demonstrate this by retrieving the point-spread function from an imaged microsphere. The noise and the influence of the microsphere size can be mitigated and sometimes completely removed from the observed images by using a maximum a posteriori estimate. However, due to the incoherent nature of the acquisition system, phase retrieval from the observed intensities will be possible only if the phase is constrained. We have used geometrical optics to model the phase of the refracted wavefront, and tested the algorithm on some simulated images.

2 - Parametric blind deconvolution for confocal laser scanning microscopy-proof of concept. P. Pankajakshan et L. Blanc-Féraud et B. Zhang et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Rapport de Recherche 6493, INRIA, avril 2008. Mots-clés : Confocal Laser Scanning Microscopy, Bayesian restoration, Blind Deconvolution, point spread function, Richardson-Lucy algorithm, Variation totale. Copyright : ARIANA/INRIA @TECHREPORT{ppankajakshan08b, author = {Pankajakshan, P. and Blanc-Féraud, L. and Zhang, B. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {Parametric blind deconvolution for confocal laser scanning microscopy-proof of concept}, year = {2008}, month = {avril}, institution = {INRIA}, type = {Research Report}, number = {6493}, url = {https://hal.inria.fr/inria-00269265}, pdf = {http://hal.inria.fr/docs/00/27/02/92/PDF/report.pdf}, keyword = {Confocal Laser Scanning Microscopy, Bayesian restoration, Blind Deconvolution, point spread function, Richardson-Lucy algorithm, Variation totale} } Résumé : Nous proposons une méthode de restauration itérative d’images de fluorescence CLSM et d’estimation paramétrique de la fonction de flou (PSF) du système d’acquisition. Le CLSM est un microscope qui balaye un échantillon en 3D et utilise une sténopée pour rejeter la lumière en dehors du point de focalisation. Néanmoins, la qualité des images souffre de deux limitations physiques. La première est due à la diffraction due au système optique et la seconde est due à la quantité réduite de lumière détectée par le tube photo-multiplicateur (PMT). Ces limitations induisent respectivement un flou et du bruit de comptage de photons. Les images peuvent alors bénéficier d’un post-traitement de restauration fondé sur la déconvolution. Le problème à traiter est l’estimation simultanée de la distribution 3D de l’échantillon des sources fluorescentes et de la PSF du microscope (i.e. de déconvolution aveugle). En utilisant un modèle de processus physique d’acquisition d’images microscopiques (CLSM), on réduit le nombre de paramètres libres décrivant la PSF et on introduit des contraintes. On introduit aussi des connaissances a priori sur l’échantillon ce qui permet de stabiliser le processus d’estimation et de favoriser la convergence. Des expériences sur des données synthétiques montrent que la PSF peut être estimée avec précision. Des expériences sur des données réelles montrent de bons resultats de déconvolution en comparaison avec le modèle théorique de la PSF du microscope. Abstract : We propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscope (CLSM) images with parametric estimation of the acquisition system’s Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the image suffers from two primary physical limitations. The first is due to the diffraction-limited nature of the optical system and the second is due to the reduced amount of light detected by the photomultiplier tube (PMT). These limitations cause blur and photon counting noise respectively. The images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observation data. We also introduce a priori knowledge of the specimen that permits stabilization of the estimation process and favorizes the convergence. Experiments on simulated data show that the PSF could be estimatedwith a higher degree of accuracy and those done on real data show very good deconvolution results in comparison to the theoretical microscope PSF model.

3 - 3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization. N. Dey et L. Blanc-Féraud et C. Zimmer et P. Roux et Z. Kam et J.C. Olivo-Marin et J. Zerubia. Rapport de Recherche 5272, INRIA, France, juillet 2004. Mots-clés : Microscopie confocale, Deconvolution, Reponse impulsionnelle, Variation totale. @TECHREPORT{5272, author = {Dey, N. and Blanc-Féraud, L. and Zimmer, C. and Roux, P. and Kam, Z. and Olivo-Marin, J.C. and Zerubia, J.}, title = {3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization}, year = {2004}, month = {juillet}, institution = {INRIA}, type = {Research Report}, number = {5272}, address = {France}, url = {http://hal.inria.fr/inria-00070726/fr/}, pdf = {https://hal.inria.fr/file/index/docid/70726/filename/RR-5272.pdf}, ps = {http://hal.inria.fr/docs/00/07/07/26/PS/RR-5272.ps}, keyword = {Microscopie confocale, Deconvolution, Reponse impulsionnelle, Variation totale} } Résumé : La microscopie confocale (Confocal laser scanning microscopy ou microscopie confocale à balayage laser) est une méthode puissante de plus en plus populaire pour l'imagerie 3D de spécimens biologiques. Malheureusement, les images acquises sont dégradées non seulement par du flou dû à la lumière provenant de zones du spécimen non focalisées, mais aussi par un bruit de Poisson dû à la détection, qui se fait à faible flux de photons. Plusieurs méthodes de déconvolution ont été proposées pour réduire ces dégradations, avec en particulier l'algorithme itératif de Richardson-Lucy, qui calcule un maximum de vraisemblance adapté à une statistique poissonienne. Mais cet algorithme utilisé comme tel ne converge pas nécessairement vers une solution adaptée, car il tend à amplifier le bruit. Si par contre on l'utilise avec une contrainte de régularisation (connaissance a priori sur l'objet que l'on cherche à restaurer, par exemple), Richardson-Lucy régularisé converge toujours vers une solution adaptée, sans amplification du bruit. Nous proposons ici de combiner l'algorithme de Richardson-Lucy avec une contrainte de régularisation basée sur la Variation Totale, dont l'effet d'adoucissement permet d'éviter les oscillations d'intensité tout en préservant les bords des objets. Nous montrons sur des images synthétiques et sur des images réelles que cette contrainte de régularisation améliore les résultats de la déconvolution à la fois qualitativement et quantitativement. Nous comparons plusieurs méthodes de déconvolution bien connues à la méthode que nous proposons, comme Richardson-Lucy standard (pas de régularisation), Richardson-Lucy régularisé avec Tikhonov-Miller, et un algorithme basé sur la descente de gradients (sous l'hypothèse d'un bruit additif gaussien). Abstract : Confocal laser scanning microscopy is a powerful and increasingly popular technique for 3D imaging of biological specimens. However the acquired images are degraded by blur from out-of-focus light and Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes a maximum likelihood estimation adapted to Poisson statistics. However this algorithm does not necessarily converge to a suitable solution, as it tends to amplify noise. If it is used with a regularizing constraint (some prior knowledge on the data), Richardson-Lucy regularized with a well-chosen constraint, always converges to a suitable solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularizing constraint based on Total Variation, whose smoothing avoids oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results both visually and using quantitative measures. We compare several well-known deconvolution methods to the proposed method, such as standard Richardson-Lucy (no regularization), Richardson-Lucy with Tikhonov-Miller regularization, and an additive gradient-based algorithm.

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