Blind depth-variant blur removal in confocal microscopy

We are interested in blind restoration of 3D confocal microscopy images. One challenging problem in this system is the depth-variant (DV) blur due to refractive index mismatch. In our work, we simplify the problem by approximating the DV point spread function (PSF) by a convex combination of a set of space-invariant (SI) PSFs. We show that each SI PSF can be approximated by a Gaussian function given by few parameters. One advantage of such an approximation is that positivity and normalization of the PSF are naturally ensured. The problem is thus reduced to the estimation of the object and the PSF parameters. We design a new criterion allowing both estimations of the object and the DV PSF, with physical constraints included. The method is validated on simulated and real confocal microscopy data.