Direct Fourier inversion and least-squares optimization method for 3D single-particle reconstruction from 2D projections acquired with cryo-electron microscopy
Single-particle reconstruction using cryo-electron microscopy allows the study of 3D molecular structures with atomic resolution. The problem of reconstructing a 3D structure from 2D projections is ill-posed, and various methods of resolving this exist. This work is a comparative study between two such methods, direct Fourier inversion (DFI) and least-squares conjugate gradient optimization of the normal equations (LSCG). While DFI demonstrates lower sensitivity to limited field of view and Gaussian noise, LSCG offers superior accuracy in resolving finer details and exhibits faster performance, particularly with increased numbers of projections and higher resolutions. Optimization strategies, such as an optimal CG early-stopping criterion, significantly enhance both methods, and explicit regularization could further improve reconstruction quality, particularly in high-noise scenarios.
Reconstruction.py provides functions for generating projections from data and the tools to create 3D/2D reconstructions from these projections.
The Reconstruction.py file can be downloaded and called with e.g. the provided iPython notebook. This code makes use of the ASPIRE and PyNUFFT packages, which can be installed from https://github.com/ComputationalCryoEM/ASPIRE-Python and https://pynufft.readthedocs.io/en/latest/ respectively.