A comparison of image restoration approaches applied to three‐dimensional confocal and wide‐field fluorescence microscopy

Abstract

SummaryWe have compared different image restoration approaches for fluorescence microscopy. The most widely used algorithms were classified with a Bayesian theory according to the assumed noise model and the type of regularization imposed. We considered both Gaussian and Poisson models for the noise in combination with Tikhonov regularization, entropy regularization, Good's roughness and without regularization (maximum likelihood estimation). Simulations of fluorescence confocal imaging were used to examine the different noise models and regularization approaches using the mean squared error criterion. The assumption of a Gaussian noise model yielded only slightly higher errors than the Poisson model. Good's roughness was the best choice for the regularization. Furthermore, we compared simulated confocal and wide-field data. In general, restored confocal data are superior to restored wide-field data, but given sufficient higher signal level for the wide-field data the restoration result may rival confocal data in quality. Finally, a visual comparison of experimental confocal and wide-field data is presented.

Characterizing the three‐dimensional organization of telomeres

“…This deconvolution method was chosen for this work because it has been shown to provide the best results (7). In this procedure we seek to find the most likely original image that could have produced the observed data.…”

“…Equation 1 is a concatenation of equations 4 and 5 in Verveer et al (7). The iterative algorithm seeks an image f that minimizes f(f) and thereby produces the most likely f that could have given rise to the measured g. Further, the deconvolution works with the constraint that the final restored image should consist of only nonnegative numbers because we cannot have a negative number of photons.…”

Generalized approach for accelerated maximum likelihood based image restoration applied to three‐dimensional fluorescence microscopy

“…They describe the random photon emission process more accurately than a Gaussian distribution. The negative log likelihood functional is given by van Kempen et al (1997) and Verveer et al (1999):…”

“…Deconvolution techniques have been shown to be beneficial to those images as well (van der Voort & Strasters, 1995;McNally et al, 1998). Comparisons between different algorithms have been made and published (Verveer et al, 1999) and a variety of commercial products are available today.…”

A Three-Dimensional Bayesian Reconstruction Method with the Point Spread Function for Micro-Rotation Sequences in Wide-Field Microscopy

“…The Bayesian inversion is a statistically sound approach for solving inverse problems for a selected noise model where a priori knowledge of the object can be taken into account. The Bayesian approach has been successful in many applications such as medical imaging [6], electron tomography [7] and 3D light microscopy with optical sectioning [8].…”