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

Deconvolution microscopy has been extensively used to improve the resolution of the wide-field fluorescent microscopy, but the performance of classical approaches critically depends on the accuracy of a model and optimization algorithms. Recently, the convolutional neural network (CNN) approaches have been studied as a fast and high performance alternative. 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 deep generators, the proposed cycleGAN approach needs only a single deep generator and a linear blur kernel, which significantly improves the robustness and efficiency 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 the penalized least squares cost as a transport cost. Experimental results using simulated and real experimental data confirm the efficacy of the algorithm.