CycleGAN with a Blur Kernel for Deconvolution Microscopy: Optimal Transport Geometry

Deconvolution microscopy has been extensively used to improve the resolution of the widefield fluorescent microscopy. However, classical deconvolution approaches require the measurement or estimation of the point spread function (PSF), and are usually computationally expensive. Recently, convolutional neural network (CNN) approaches have been extensively studied as fast and high performance alternatives. Unfortunately, the CNN approaches usually require matched high resolution images for supervised training. In this paper, we present a novel unsupervised cycle-consistent generative adversarial network (cycleGAN) with a linear blur kernel, which can be used for both blind- and non-blind image deconvolution. In contrast to the conventional cycleGAN approaches that require two generators, the proposed cycleGAN approach needs only a single generator, which significantly improves the robustness of network training. We show that the proposed architecture is indeed a dual formulation of an optimal transport problem that uses a special form of penalized least squares as transport cost. Experimental results using simulated and real experimental data confirm the efficacy of the algorithm.