A multi-scale geometric flow method for molecular structure reconstruction

We have previously reported an L 2 -gradient flow (L2GF) method for cryoelectron tomography and single-particle reconstruction, which has a reasonably good performance. The aim of this paper is to further upgrade both the computational efficiency and accuracy of the L2GF method. In a finite-dimensional space spanned by the radial basis functions, a minimization problem combining a fourth-order geometric flow with an energy decreasing constraint is solved by a bi-gradient method. The bi-gradient method involves a free parameter β ∈ [0, 1]. As β increases from 0 to 1, the structures of the reconstructed function from coarse to fine are captured. The experimental results show that the proposed method yields more desirable results.