Single-molecule localization microscopy is a widely used technique in biological research for measuring the nanostructures of samples smaller than the diffraction limit. This study uses multifocal plane microscopy and addresses the three-dimensional (3D) single-molecule localization problem, where lateral and axial locations of molecules are estimated. However, when multifocal plane microscopy is used, the estimation accuracy of 3D localization is easily deteriorated by the small lateral drifts of camera positions. A 3D molecule localization problem was presented along with the lateral drift estimation as a compressed sensing problem. A deep neural network (DNN) was applied to solve this problem accurately and efficiently. The results show that the proposed method is robust to lateral drift and achieves an accuracy of 20 nm laterally and 50 nm axially without an explicit drift correction.

单分子定位显微镜是生物学研究中广泛使用的技术，用于测量小于衍射极限的样品的纳米结构。这项研究使用多焦点平面显微镜并解决了三维（3D）单分子定位问题，其中估计了分子的横向和轴向位置。但是，当使用多焦点平面显微镜时，由于相机位置的横向偏移较小，因此3D定位的估计精度容易降低。提出了3D分子定位问题以及横向漂移估计，将其作为压缩感测问题。应用了深度神经网络（DNN）来准确，有效地解决此问题。