A very fast iterative algorithm for TV-regularized image reconstruction with applications to low-dose and few-view CT

TL;DR

This paper introduces a rapid iterative algorithm for TV-regularized image reconstruction in low-dose and few-view CT, leveraging primal-dual methods and FBP preconditioning for fast convergence.

Contribution

It presents a novel, fast primal-dual iterative algorithm that incorporates FBP preconditioning, significantly accelerating TV-regularized CT image reconstruction.

Findings

Algorithm converges rapidly to the exact minimizer.

Preconditioning with FBP filter improves convergence speed.

Applicable to low-dose and few-view CT scenarios.

Abstract

This paper concerns iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with the Total Variation (TV) penalty. We propose a very fast iterative algorithm to solve this problem. The algorithm derivation is outlined as follows. First, the original minimization problem is reformulated into the saddle point (primal-dual) problem by using the Lagrangian duality, to which we apply the first-order primal-dual iterative methods. Second, we precondition the iteration formula using the ramp flter of Filtered Backprojection (FBP) reconstruction algorithm in such a way that the problem solution is not altered. The resulting algorithm resembles the structure of so-called iterative FBP algorithm, and it converges to the exact minimizer of cost function very fast.