Poisson-Gaussian noise parameter estimation in fluorescence microscopy imaging

International audienceIn this paper, we present a new fully automatic approach for noise parameter estimation in the context of fluorescence imaging systems. In particular, we address the problem of Poisson-Gaussian noise modeling in the nonstationary case. In microscopy practice, the nonstationarity is due to the photobleaching effect. The proposed method consists of an adequate moment based initialization followed by Expectation-Maximization iterations. This approach is shown to provide reliable estimates of the mean and the variance of the Gaussian noise and of the scale parameter of Poisson noise, as well as of the photobleaching rates. The algorithm performance is demonstrated on both synthetic and real fluorescence microscopy image sequences

Likelihood inference for particle location in fluorescence microscopy

We introduce a procedure to automatically count and locate the fluorescent particles in a microscopy image. Our procedure employs an approximate likelihood estimator derived from a Poisson random field model for photon emission. Estimates of standard errors are generated for each image along with the parameter estimates, and the number of particles in the image is determined using an information criterion and likelihood ratio tests. Realistic simulations show that our procedure is robust and that it leads to accurate estimates, both of parameters and of standard errors. This approach improves on previous ad hoc least squares procedures by giving a more explicit stochastic model for certain fluorescence images and by employing a consistent framework for analysis.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS299 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for error removal. Results on both simulated data and real data captured using our laser FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use

Quantum Theory of Superresolution for Two Incoherent Optical Point Sources

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern farfield superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation from the far field almost as precisely as conventional methods do for isolated sources, rendering Rayleigh's criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.Comment: 18 pages, 11 figures. v1: First draft. v2: Improved the presentation and added a section on the issues of unknown centroid and misalignment. v3: published in Physical Review