Optimized L₁-norm smoothing gradient improves electron tomography's tilt series alignment with both localized and...

Cryo-electron tomography (cryo-ET) is a crucial technique for imaging three-dimensional (3D) biological ultrastructure, where tilt series alignment is a vital step. The tilt series alignment primarily utilizes localized or virtual fiducial markers to establish correlations among different projections, and bundle adjustment is employed to calibrate the projection parameters for high-resolution reconstruction. However, due to the localization error and non-uniform drifting of fiducial markers, the alignment process will inevitably be adversely impacted by observation noise and outliers, necessitating increasingly robust projection parameter estimation. Here, we employ an optimized L₁-norm smoothing gradient approach to align the tilt series. Various step selection criteria are examined, including the Wolfe and Goldstein criteria, to explore the sufficient descent condition. We propose a preliminary mathematical convergence result of the two criteria, and discuss the convergence under suitable initialization for the model considered in the article. Comprehensive experiments demonstrate the superior performance of our method in simulated data under various noise and outlier conditions, showing further improvement in real-world tomogram reconstruction.