Computed tomography (CT) has been widely applied in medical imaging and industry for over decades. CT reconstruction from limited projection data is of particular importance. The total variation or l1-norm regularization has been widely used for image reconstruction in computed tomography (CT). Images in computed tomography (CT) are mostly piece-wise constant so the gradient images are considered as sparse images. The l0-norm of the gradients of an image provides a measurement of the sparsity of gradients of the image. However, the l0-norm regularization problem is NP hard. In this talk, we present two new models for CT image reconstruction from limited-angle projections. In one model we propose the smoothed l0-norm and l1-norm regularization using the nonmonotone alternating direction algorithm. In the other model we propose a combined l1-norm and l0-norm regularization model for better edge preserving
