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Three-dimensional images of confocal laser scanning microscopy suffer from a depth-variant blur, due to refractive index mismatch between the different mediums composing the system as well as the specimen, leading to optical aberrations. Our goal is to develop an image restoration method for 3D confocal microscopy taking into account the blur variation with depth. The difficulty is that optical aberrations depend on the refractive index of the biological specimen. The depth-variant blur function or the Point Spread Function (PSF) is thus different for each observation. A blind or semi-blind restoration method needs to be developed for this system. For that purpose, we use a previously developed algorithm for the joint estimation of the specimen function (original image) and the 3D PSF, the continuously depth-variant PSF is approximated by a convex combination of a set of space-invariant PSFs taken at different depths. We propose to add to that algorithm a pupil-phase constraint for the PSF estimation, given by the the optical instrument geometry. We thus define a blind estimation algorithm by minimizing a regularized criterion in which we integrate the Gerchberg-Saxton algorithm allowing to include these physical constraints. We show the efficiency of this method relying on some numerical tests.

Depth-variant blind restoration with pupil-phase constraints for 3D confocal microscopy