Poisson Point Processes for Solving Stochastic Inverse Problems in Fluorescence Microscopy
Despite revolutionary developments in fluorescence based optical microscopy imaging, the quality of the images remains fundamentally limited by diffraction and noise. Hence, deconvolution methods are often applied to obtain better estimates of the biologi
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Abstract. Despite revolutionary developments in fluorescence based optical microscopy imaging, the quality of the images remains fundamentally limited by diffraction and noise. Hence, deconvolution methods are often applied to obtain better estimates of the biological structures than the measured images are providing prima facie, by reducing blur and noise as much as possible through image postprocessing. However, conventional deconvolution methods typically focus on accurately modeling the point-spread function of the microscope, and put less emphasis on properly modeling the noise sources. Here we propose a new approach to enhancing fluorescence microscopy images by formulating deconvolution as a stochastic inverse problem. We solve the problem using Poisson point processes and establish a connection between the classical SheppVardi algorithm and probability hypothesis density filtering. Results of preliminary experiments on image data from various biological applications indicate that the proposed method compares favorably with existing approaches in jointly performing deblurring and denoising. Keywords: Stochastic reconstruction · Poisson point process · Probability hypothesis density filter · Fluorescence microscopy · Deconvolution
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Introduction
Fluorescence microscopy imaging is an indispensable tool in numerous biological studies for visualizing (intra)cellular structures and dynamic processes. However, the quality of the acquired images is often rather poor, mainly due to low photon counts and the usage of diffraction-limited optics. This is especially true in singlemolecule imaging experiments, where the objects of interest (generally termed “particles”) are smaller than the optical resolution of the microscope and the fluorescence signal is weak. As a result, fluorescently labeled vesicles, peroxisomes, or other particles are typically rendered as blurred spots with Gaussian-like intensity profiles, severely corrupted by Poisson noise [1,2]. But also in the case of imaging larger objects, such as microtubules and actin filaments within cells, c Springer International Publishing Switzerland 2016 G. Hua and H. J´ egou (Eds.): ECCV 2016 Workshops, Part I, LNCS 9913, pp. 326–338, 2016. DOI: 10.1007/978-3-319-46604-0 24
Poisson Point Processes for Solving Stochastic Inverse Problems
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or the dendritic and axonal arbors of neurons, the effects of noise and blurring may adversely affect subsequent analyses. The main sources of noise in fluorescence microscopy are the signal itself (photon shot noise) and the digital imaging electronics. The mechanics of both noise sources is well understood and the statistical distributions of noise are known [3,4]. The signal-dependent noise is described by a Poisson distribution, while the noise arising from the imaging system often follows a Gaussian distribution. In practice, especially with low-excitation or single-molecule fluorescence imaging, the signal-dependent noise dominates, and the Gaussian noise caused by the imaging device can be ignored. The latter source of noise
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