A Smoothed l0-Norm and l1-Norm Regularization Algorithm for Computed Tomography

Jiehua Zhu,Xiezhang Li

doi:10.1155/2019/8398035

Abstract

The nonmonotone alternating direction algorithm (NADA) was recently proposed for effectively solving a class of equality-constrained nonsmooth optimization problems and applied to the total variation minimization in image reconstruction, but the reconstructed images suffer from the artifacts. Though by the l0-norm regularization the edge can be effectively retained, the problem is NP hard. The smoothed l0-norm approximates the l0-norm as a limit of smooth convex functions and provides a smooth measure of sparsity in applications. The smoothed l0-norm regularization has been an attractive research topic in sparse image and signal recovery. In this paper, we present a combined smoothed l0-norm and l1-norm regularization algorithm using the NADA for image reconstruction in computed tomography. We resolve the computation challenge resulting from the smoothed l0-norm minimization. The numerical experiments demonstrate that the proposed algorithm improves the quality of the reconstructed images with the same cost of CPU time and reduces the computation time significantly while maintaining the same image quality compared with the l1-norm regularization in absence of the smoothed l0-norm.

Highlights

Statistical and iterative reconstruction algorithms in computed tomography (CT) are widely applied since they yield more accurate results than analytic approaches for low-dose and limited-view reconstruction
The numerical experiments demonstrate that the proposed algorithm improves the quality of the reconstructed images with the same cost of CPU time and reduces the computation time significantly while maintaining the same image quality compared with the l1-norm regularization in absence of the smoothed l0-norm
The purposes of this paper are multifold: (i) Presenting a combined sl0-norm and l1-norm regularization algorithm for image reconstruction in CT: The proposed algorithm is unique in the following aspects: A new parameter is introduced to balance the sl0-norm and l1-norm terms; two-norm regularization is combined in one Lagrangian object function to be minimized (ii) Adopting a newly developed alternating direction method nonmonotone alternating direction algorithm (NADA) to efficiently solve minimization (iii) Resolving the computation challenge problem caused from the sl0-norm minimization

Summary

A Smoothed l0-Norm and l1-Norm Regularization Algorithm for Computed Tomography

The nonmonotone alternating direction algorithm (NADA) was recently proposed for effectively solving a class of equalityconstrained nonsmooth optimization problems and applied to the total variation minimization in image reconstruction, but the reconstructed images suffer from the artifacts. Though by the l0-norm regularization the edge can be effectively retained, the problem is NP hard. We present a combined smoothed l0-norm and l1-norm regularization algorithm using the NADA for image reconstruction in computed tomography. We resolve the computation challenge resulting from the smoothed l0-norm minimization. The numerical experiments demonstrate that the proposed algorithm improves the quality of the reconstructed images with the same cost of CPU time and reduces the computation time significantly while maintaining the same image quality compared with the l1-norm regularization in absence of the smoothed l0-norm

Introduction

Background and Notations

Numerical Experiments and Results

Discussions and Conclusions