Publications about total variation regularization

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• 1 PhD Thesis and Habilitation
• 2 Conference articles

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PhD Thesis and Habilitation

1 - Blind Deconvolution for Confocal Laser Scanning Microscopy. P. Pankajakshan. PhD Thesis, Universite de Nice Sophia Antipolis, December 2009. Keywords : Confocal Laser Scanning Microscopy, Blind Deconvolution, point spread function, Maximum likelihood estimation , total variation regularization. @PHDTHESIS{PankajakshanThesis09, author = {Pankajakshan, P.}, title = {Blind Deconvolution for Confocal Laser Scanning Microscopy}, year = {2009}, month = {December}, school = {Universite de Nice Sophia Antipolis}, url = {http://tel.archives-ouvertes.fr/tel-00474264/fr/}, keyword = {Confocal Laser Scanning Microscopy, Blind Deconvolution, point spread function, Maximum likelihood estimation , total variation regularization} } Résumé : La microscopie confocale à balayage laser, est une technique puissante pour étudier les spécimens biologiques en trois dimensions (3D) par sectionnement optique. Elle permet d’avoir des images de spécimen vivants à une résolution de l’ordre de quelques centaines de nanomètres. Bien que très utilisée, il persiste des incertitudes dans le procédé d’observation. Comme la réponse du système à une impulsion, ou fonction de flou (PSF), est dépendante à la fois du spécimen et des conditions d’acquisition, elle devrait être estimée à partir des images observées du spécimen. Ce problème est mal posé et sous déterminé. Pour obtenir une solution, il faut injecter des connaisances, c’est à dire, a priori dans le problème. Pour cela, nous adoptons une approche bayésienne. L’état de l’art des algorithmes concernant la déconvolution et la déconvolution aveugle est exposé dans le cadre d’un travail bayésien. Dans la première partie, nous constatons que la diffraction due à l’objectif et au bruit intrinsèque à l’acquisition, sont les distorsions principales qui affectent les images d’un spécimen. Une approche de minimisation alternée (AM), restaure les fréquences manquantes au-delà de la limite de diffraction, en utilisant une régularisation par la variation totale sur l’objet, et une contrainte de forme sur la PSF. En outre, des méthodes sont proposées pour assurer la positivité des intensités estimées, conserver le flux de l’objet, et bien estimer le paramètre de la régularisation. Quand il s’agit d’imager des spécimens épais, la phase de la fonction pupille, due aux aberrations sphériques (SA) ne peut être ignorée. Dans la seconde partie, il est montré qu’elle dépend de la difference à l’index de réfraction entre l’objet et le milieu d’immersion de l’objectif, et de la profondeur sous la lamelle. Les paramètres d’imagerie et la distribution de l’intensité originelle de l’objet sont calculés en modifiant l’algorithme AM. Due à la nature de la lumière incohérente en microscopie à fluorescence, il est possible d’estimer la phase à partir des intensités observées en utilisant un modèle d’optique géométrique. Ceci a été mis en évidence sur des données simulées. Cette méthode pourrait être étendue pour restituer des spécimens affectés par les aberrations sphériques. Comme la PSF varie dans l’espace, un modèle de convolution par morceau est proposé, et la PSF est approchée. Ainsi, en plus de l’objet, il suffit d’estimer un seul paramétre libre. Abstract : Confocal laser scanning microscopy is a powerful technique for studying biological specimens in three dimensions (3D) by optical sectioning. It permits to visualize images of live specimens non-invasively with a resolution of few hundred nanometers. Although ubiquitous, there are uncertainties in the observation process. As the system’s impulse response, or point-spread function (PSF), is dependent on both the specimen and imaging conditions, it should be estimated from the observed images in addition to the specimen. This problem is ill-posed, under-determined. To obtain a solution, it is necessary to insert some knowledge in the form of a priori and adopt a Bayesian approach. The state of the art deconvolution and blind deconvolution algorithms are reviewed within a Bayesian framework. In the first part, we recognize that the diffraction-limited nature of the objective lens and the intrinsic noise are the primary distortions that affect specimen images. An alternative minimization (AM) approach restores the lost frequencies beyond the diffraction limit by using total variation regularization on the object, and a spatial constraint on the PSF. Additionally, some methods are proposed to ensure positivity of estimated intensities, to conserve the object’s flux, and to well handle the regularization parameter. When imaging thick specimens, the phase of the pupil function due to spherical aberration (SA) cannot be ignored. It is shown to be dependent on the refractive index mismatch between the object and the objective immersion medium, and the depth under the cover slip. The imaging parameters and the object’s original intensity distribution are recovered by modifying the AM algorithm. Due to the incoherent nature of the light in fluorescence microscopy, it is possible to retrieve the phase from the observed intensities by using a model derived from geometrical optics. This was verified on the simulated data. This method could also be extended to restore specimens affected by SA. As the PSF is space varying, a piecewise convolution model is proposed, and the PSF approximated so that, apart from the specimen, it is sufficient to estimated only one free parameter.

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2 Conference articles

1 - Blind deconvolution for diffraction-limited fluorescence microscopy. P. Pankajakshan and B. Zhang and L. Blanc-Féraud and Z. Kam and J.C. Olivo-Marin and J. Zerubia. In Proc. IEEE International Symposium on Biomedical Imaging (ISBI), pages 740-743, Paris, France, May 2008. Keywords : Confocal microscopy, 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 = {May}, 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 = {Confocal microscopy, 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.

2 - A deconvolution method for confocal microscopy with total variation regularization. N. Dey and L. Blanc-Féraud and C. Zimmer and Z. Kam and J.C. Olivo-Marin and J. Zerubia. In Proc. IEEE International Symposium on Biomedical Imaging (ISBI), Arlington, USA, April 2004. Keywords : 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 = {April}, 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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