Computed tomography image reconstruction from few views via Log-norm total variation minimization

In this paper, we propose an iterative algorithm for the computed tomography (CT) image reconstruction from severely under-sampled data. Instead of using ℓ₁-norm sparse regularization, the proposed algorithm utilizes the non-convex Log-norm penalty (LSP) of the gradient-magnitude images (GMI), which can overcome the disadvantages tendency of uniformly penalize the signal amplitude and underestimate the high-amplitude components. To rise to the challenges introduced by the non-convex regularization, we employ the difference of convex framework to decompose the objective function into a separable ℓ₁ type problem and draw its connection to the alternating direction method (ADM). We show that any cluster points of the sequence generated by the proposed algorithm converge to a stationary point. The simulation result demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.