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Image reconstruction from few views by ℓ0-norm optimization

In the medical computer tomography (CT) field, total variation (TV), which is the ℓ1-norm of the discrete gradient transform (DGT), is widely used as regularization based on the compressive sensing (CS) theory. To overcome the TV model's disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, an iterative algorithm based on the ℓ0-norm optimization of the DGT is proposed. In order to rise to the challenges introduced by the ℓ0-norm DGT, the algorithm uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding (IHT) algorithm, whose convergence and effective efficiency have been theoretically proven. The simulation demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.