Imagerie rétinienne à haute résolution : restauration d`images

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