Imagerie rétinienne à haute résolution : restauration d’images corrigées par Optique Adaptative Laurent Mugnier ONERA / DOTA / Haute Résolution Angulaire 1 Organisation de l ONERA Président Directeur Général Délégué Général Sécurité Industrielle et Défense Denis Maugars Michel Boisson Ressources Humaines Directeur Scientifique Général Directeur Technique Général Développement Commercial et Valorisation Affaires Internationales Véronique Padoan Emmanuel Rosencher Thierry Michal Michel Humbert Dominique Nouailhas Mécanique des Fluides et Énergétique Jean-Jacques Thibert 22 CNES / 5 départements 458 352 Physique Pierre Touboul 4 départements Matériaux et Structures Daniel Abbé 3 départements Traitement de l Information et Systèmes Claude Barrouil 3 départements 405 223 236 5 départements Grands Moyens Techniques Patrick Wagner HRA : les Hommes et les Femmes 3 ! 17 ingénieurs et cadres (dont 12 docteurs) ! 1 technicienne ! 10 doctorants ! 1 ingénieur en formation par alternance ! Unité Haute Résolution Angulaire (HRA), Châtillon Equipe Haute Résolution Angulaire λ/ro λ/D Système optique parfait En présence de turbulence Etude et développement des méthodes et des instruments permettant d'approcher la limite de résolution théorique de la diffraction en dépit des aberrations aléatoires ! Optique adaptative : astronomie, défense, télécom optiques, imagerie de la rétine ! Instruments multi-pupilles : concepts & système, senseur de franges, cophasage ! Traitement des données, restauration d images (OA et IMP) ! Analyse de front d'onde ! Propagation optique à travers la turbulence ! Effets aéro-optiques 4 Les principales coopérations scientifiques Organismes étatiques • GIS Phase • European Southern Observatory • Centre National d Etudes Spatiales • Laboratoire de Traitement et de Transport de l Information (Paris XIII) • Hôpital des Quinze-Vingts (convention Œil-HRS) Industriels • Cilas, Imagine Eyes, Shaktiware • Sagem, Tosa, TAS, Astrium 5 Banc d’optique adaptive (BOA) pour l’observation des satellites LEO 6 BOA à l OHP : Optique adaptative et déconvolution Observation de Ganymède à l Observatoire de Haute Provence Image sans OA Image avec OA Image obtenue par Image déconvoluée les sondes Voyager et Galiléo par MISTRAL à la limite de diffraction (code HRA) du télescope Base de données JPL MISTRAL = Myopic Iterative STep-preserving Restoration Algorithm (Mugnier et coll., JOSA A, 2004) Images obtenues à l OHP (1.52 m) avec le banc d OA de l ONERA (BOA) λ = 0.85 mm - D/r0 =23 28 septembre 1997 - 20:18 UT 7 Retinal imaging: context Medical context: Need for early diagnosis and treatment follow-up tools, with a cellular resolution (a few µm) ! Scientific challenges: ! Compensate for the poor optical quality of the eye => Adaptive Optics (AO) ! Restore the lateral resolution, in spite of ! AO’s partial correction, with limited flux, ! retina’s thickness and scattering ! => 2D image restoration Obtain an axial resolution (3D imaging) => AO+SLO or +OCT or … ! 8 Imagerie « simple » instrument • Mouvements de l œil • Aberrations évolutives (film lacrymal, …) OA Imagerie avec optique adaptative instrument Analyseur de surface d onde Outline Restoration of AO-corrected retinal images: ! • (Context) • Méthod developed: " 2D image model of a 3D object " Marginal estimation vs joint estimation (supervised) " Unsupervised (“fully automatic”) marginal estimation • 12 Application to experimental images Most deconvolution techniques boil down to the minimization (or maximization) of a criterion. An important task is the definition of a suitable criterion for the given inverse problem. Following the Bayesian12 maximum a posteriori (MAP) approach, the deconvolution problem can be stated as follows: we look for the most likely object ô, given the observed image i and our prior information on o, which is summarized by a probability density p$o%. This reads as Specifics of retinal imaging for image restoration Short-exposure, noisy images ô = arg max p$o&i% = arg max p$i&o% " p$o%. => Preliminary step = image registration and mosaicing; Equivalently, ô can be defined as the object that mini- ! o o mizes a compound criterion J$o% defined as follows: ! 2D images of a thick (3D) object: many planes of the retina contribute to a given image => lack of information; ! Poorly known Point Spread Function (PSF): residual aberrations, scattering => classical deconvolution (w/ known PSF) not applicable ! « Myopic » deconvolution: PSF unknown 13 Fig. 1. Illustration of the 3D image formation for three object planes. The object is on the left, and the image is on the right. The system is composed of the eye and the optical system (including the AO). In image i1, object o1 is focused; o2 and o3 are defocused. Images i2 and i3 are not represented here. • search for object and PSF • conventional method: joint estimation of object and PSF • constraints usually used in astronomy (positivity, support) are not applicable terion Jo, which is chosen PSD model PSD$f% = E(&o$f% where f is the spa (it is typically a co of the object, and avoid the divergen verse of the charac the parameters of tomatically (i.e., in by a maximum-li method developed context. The disadvantag of a quadratic regu with sharp edges that it tends to ove use an edge-prese gradients and line ensures a good sm noise), and the line large gradients (i. and Sauer.18 Such L2 – L1 for short.19 tropic version of th context of robust for image restora through turbulenc from L2 to L1 is c (Some) approaches for myopic deconvolution ! Explicit modelling of the 3D imaging process ! + simplified object model: axially invariant (within depth of focus) ≈70 µm& => image model: ! i o ∑α h(ϕ i 0 + Δϕ i ) n i = PSF to be identified Myopic deconvolution: ! • Joint deconvolution: conventional in astronomy. Support, positivity constraints inapplicable • Marginalization : estimate «only» the PSF. most likely PSF on average for all possible objects (in a given class): 14 Joint estimation of the PSF and the object (oˆ, αˆ ) JMAP = argmax p(o,{α i } i) Traditional blind/myopic deconvolution: o,α In the Fourier domain, the criterion reads: 1 J JMAP (o, α ) = 2S n ~ ( f ) − o~ ( f ) 2 2 o ~ 1 ~ m ~ (f) + i ( f ) − h ( α , f ) o where ∑f ∑ S (f) € 2 f o Fidelity to the data i = h ∗o + n h(x, y,ϕ) = ∑ α i hi (x, y) i hi (x, y) : ϕ0 + ϕdefoc (zi ) Object regularization term By substituting the object minimizing JJMAP (Wiener estimate for current α), we obtain: € 2 ˜ ˜ ˜ i ( f ) − h ( α , f ) o ( f ) 1 m J JMAP (ô(α ), α ) = ∑ +C 2 ˜ 2 f h (α , f ) + S S ( f ) n Hyperparameters Sn and So assumed known 15 € o