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 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 Shepp-Vardi 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.