Computational inversion of electron micrographs using L2‐gradient flows—convergence analysis

A gradient flow‐based explicit finite element method (L2GF) for reconstructing the 3D density function from a set of 2D electron micrographs has been proposed in recently published papers. The experimental results showed that the proposed method was superior to the other classical algorithms, especially for the highly noisy data. However, convergence analysis of the L2GF method has not been conducted. In this paper, we present a complete analysis on the convergence of L2GF method for the case of using a more general form regularization term, which includes the Tikhonov‐type regularizer and modified or smoothed total variation regularizer as two special cases. We further prove that the L²‐gradient flow method is stable and robust. These results demonstrate that the iterative variational reconstruction method derived from the L²‐gradient flow approach is mathematically sound and effective and has desirable properties. Copyright © 2013 John Wiley & Sons, Ltd.