Microscopy Image Restoration with Deep Wiener-Kolmogorov filters

Microscopy is a powerful visualization tool in biology, enabling the study of cells, tissues, and the fundamental biological processes. Yet, the observed images of the objects at the micro-scale suffer from two major inherent distortions: the blur caused by the diffraction of light, and the background noise caused by the imperfections of the imaging detectors. The latter is especially severe in fluorescence and in confocal microscopes, which are known for operating at the low photon count with the Poisson noise statistics. Restoration of such images is usually accomplished by image deconvolution, with the nature of the noise statistics taken into account, and by solving an optimization problem given some prior information about the underlying data (i.e., regularization). In this work, we propose a unifying framework of algorithms for Poisson image deblurring and denoising. The algorithms are based on deep learning techniques for the design of learnable regularizers paired with an appropriate optimization scheme. Our extensive experimentation line showcases that the proposed approach achieves superior quality of image reconstruction and beats the solutions that rely on deep learning or on the optimization schemes alone. Moreover, several implementations of the proposed framework demonstrate competitive performance at a low computational complexity, which is of high importance for real-time imaging applications.