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