A Smoothed l_0-Norm and l_1-Norm Regularization Algorithm for Computed Tomography

摘要

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 l_0-norm regularization the edge can be effectively retained, the problemisNP hard.The smoothed l_0-normapproximates the l_0-normas a limit of smooth convex functions and provides a smooth measure of sparsity in applications.The smoothed l_0-normregularization has been an attractive research topic in sparse image and signal recovery. In this paper, we present a combined smoothed l_0-norm and l_1-norm regularization algorithm using the NADA for image reconstruction in computed tomography. We resolve the computation challenge resulting from the smoothed l_0-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 l_1-norm regularization in absence of the smoothed l_0-norm.