Single-molecule localization by voxel-wise regression using convolutional neural network

Single-molecule localization microscopy is widely used in biological research for measuring the nanostructures of samples smaller than the diffraction limit. In this paper, a novel method for regression of the coordinates of molecules for multifocal plane microscopy is presented. A regression problem for the target space is decomposed into regression problems for small subsets of the target space. Then, a deep neural network is used to solve these problems. By decomposing the regression problem, a fully convolutional neural network can be used to solve the regression problems. The computation of the network is efficient, and a simple and parameter-free loss function can be used to train the network. The proposed algorithm is validated by both simulated and real data obtained by quad-plane microscopy.