FFT-based methods for nonlinear image restoration in confocal microscopy

Abstract

Recently we developed a new method for attenuation correction in 3D imaging by a confocal scanning laser microscope (CSLM) in the (epi)fluorescence mode. The fundamental element in our approach consisted of multiplying the measured fluorescent intensity by a correction factor involving a convolution integral of this intensity, which can be computed efficiently by the fast Fourier transform (FFT). The resulting algorithm is one or two orders of magnitude faster than an existing iterative method, but it was found to have a somewhat smaller accuracy. In this paper we improve on this latter point by reformulating the problem as a statistical estimation problem. In particular, we derive first-order-moment and cumulant estimators leading to a nonlinear integral equation for the unknown fluorescent density, which is solved by an iterative method in which in each step a discrete convolution is performed by using the FFT. We find that only a few iterations are needed. It is shown that the estimators proposed here are more accurate than the existing iterative method, while they retain the advantage in computational efficiency of the FFT-based approach.