Gradient-flow-based semi-implicit finite-element method and its convergence analysis for image reconstruction

Abstract

In this paper, we present a novel and effective L2-gradient-flow-based semi-implicit finite-element method for solving a variational problem of image reconstruction. The method is applicable to several data scenarios, especially for the contaminated data detected from uniformly sparse or randomly distributed projection directions. We also give a complete and rigorous proof for the convergence of the semi-implicit finite-element method, in which the convergence does not rely on the choices of the regularization parameter and the temporal step size. The experimental results show that our method has more desirable performance comparing with other reconstruction methods in solving a number of challenging reconstruction problems.