SummaryIn 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 RichardsonLucy 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.

Background The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. Methods The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed. Results We tested the three estimators on simulated data, real‐world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real‐world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators. Conclusions We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators. Cytometry 39:300–305, 2000 © 2000 Wiley‐Liss, Inc.

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