A quantative comparison of two restoration methods as applied to confocal microscopy

A quantitative comparison of two restoration methods as applied to confocal microscopy, Proc. 1. Introduction The main contribution of the confocal microscope to microscopy is that it provides a practical method to obtain microscopic volume images. Although a confocal microscope is a true volume imager, its imaging properties give rise to a blurring phenomenon similar to that of a conventional microscope, but with a reduced range. The resulting distortions hamper subsequent quantitative analysis. Therefore, operations that invert the distortions of the microscope may improve these analyses. In previous work [1], the iterative constrained Tikhonov-Miller (ICTM) inversion was used to restore diffraction-induced distortions. Quantitative texture measurements, based on the grey value distance transform (GDT) [2], showed that the results improved when applied to images after restoration. The use of the ICTM restoration method was motivated by the linear system model of the imaging properties of a confocal microscope. In this model, the image is a convolution of the object with the microscopes point spread function and distorted by additive noise. However in images with a low signal-to-noise ratio (SNR), this additive noise model is a poor description of the actual photon-limited image recording. Under these circumstances, the noise characteristics are best described by a Poisson process, which motivates the use of restoration methods optimized for Poisson noise distorted images. We have compared the ICTM inversion with the expectation-maximization algorithm for computing the maximum likelihood estimator (EM-MLE) for the intensity of a Poisson process