Robust projection parameter calibration in cryo-ET with L1-norm optimization

Fiducial marker-based alignment in cryo-electron tomography (cryo-ET) has been extensively studied over a long period. The calibration of projection parameters using nonlinear least squares technique methodologies stands as the ultimate and pivotal stage in the alignment procedure. The efficacy of calibration is substantially impacted by noise and outliers in the marker data obtained from previous steps. Several robust fitting methods have been explored and implemented to address this issue by improving marker data or assigning weights to markers. However, these methods have their own limitations and often assume general Gaussian noise assumption, which may not accurately represent the distribution of noise and outliers in the marker data. In this work, we propose a robust projection parameter calibration model based on $L_1$-norm optimization under Laplace noise assumption in order to overcome the limitations of existing methods. To efficiently solve the problem, we also design a faster and stabler first-order non-sparse method based on smooth approximation strategy. Additionally, we introduce subgradient and subdifferential for mathematical analysis. The accuracy, robustness, and efficacy of our approach are demonstrated through both simulated and real-world experiments.