Few views image reconstruction using alternating direction method via ℓ 0 ‐norm minimization

In the medical computer tomography field, total variation (TV), which is theℓ 1 ‐norm of the gradient‐magnitude images, is widely used as the regularization based on the compressive sensing theory. To overcome the TV model's disadvantageous tendency of uniformly penalize the image gradient and over smooth the low‐contrast structures, an iterative algorithm based on theℓ 0 ‐norm optimization of the finite difference is proposed. To rise to the challenges introduced by theℓ 0 ‐norm minimization, the algorithm uses the alternating direction method to solve the unconstrained augmented Lagrangian function, which involves a hard thresholding method, a linearization and proximal points technique for each subproblem. The simulation demonstrates the conclusions and indicates that the algorithm proposed in this article can obviously improve the reconstruction quality. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 215–223, 2014