A quantitative comparison of image restoration methods for confocal microscopy

In this paper, we compare the performance of three iterative methods for image restoration: the Richardson–Lucy algorithm, the iterative constrained Tikhonov–Miller algorithm (ICTM) and the Carrington algorithm. Both the ICTM and the Carrington algorithm are based on an additive Gaussian noise model, but differ in the way they incorporate the non‐negativity constraint. Under low light‐level conditions, this additive (Gaussian) noise model is a poor description of the actual photon‐limited image recording, compared with that of a Poisson process. The Richardson–Lucy algorithm is a maximum likelihood estimator for the intensity of a Poisson process. We have studied various methods for determining the regularization parameter of the ICTM and the Carrington algorithm and propose a (Gaussian) prefiltering to reduce the noise sensitivity of the Richardson–Lucy algorithm. The results of these algorithms are compared on spheres convolved with a point spread function and distorted by Poisson noise. Our simulations show that the Richardson–Lucy algorithm, with Gaussian prefiltering, produces the best result in most of the tests. Finally, we show an example of how restoration methods can improve quantitative analysis: the total amount of fluorescence inside a closed object is measured in the vicinity of another object before and after restoration.