An Analytical Method of Automatic Alignment for Electron Tomography
In the imaging process for nanometer-scale electron tomography, misalignment between the actual projection parameters and the theoretical ones is inevitable due to mechanical precision of the instrument. Effective alignment remains a challenge. Currently, marker-based alignment approaches complicate the sample preparation process and worsen the sample shrinking issue. Marker-free approaches suffer from either low accuracy or long computation time.
In this paper, we formulate an analytical problem for marker-free alignment by minimizing the reprojection error. The reprojection error involves the projection operator, which is a complicated functional with the projection parameters as the variables. To solve this optimization problem, we derive a gradient-based approach by decomposing the original problem with auxiliary parameters and by linearizing a subproblem with Taylor expansion. The approach is computational friendly, especially when comparing to an exhaustively parameter tuning approach in previous practice. The results show that our method is capable of accurate alignment without fiducial markers and obtains a 16.7\(\times \) speedup over the existing exhaustive approach, which makes fine reconstruction of ROI almost instantly ready after data collection. A preliminary FPGA design for the method’s bottleneck process shows 6.6\(\times \) speed-up over well-optimized GPU program.
KeywordsElectron tomography Automatic alignment Functional optimization
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