A cascading l0 regularization reconstruction method in nonsubsampled contourlet domain for limited-angle CT

In some computed tomography (CT) practical applications, the projection data is incomplete, which makes some limited-angle artifacts presented in the reconstructed image. Total variation (TV) regularization method is used to suppress the artifacts, but the edge of reconstructed image is distorted or some tiny details are missed. To preserve the edge of reconstructed image, a cascading ℓ0 regularization-based reconstruction model in nonsubsampled contourlet transform (NSCT) domain is proposed, which considers both the directional peculiarity of artifacts and the smooth of low frequency of the reconstructed image. In the proposed reconstruction model, a ℓ0 regularization term in the high frequency is used to suppress the artifacts and noise, and a ℓ0 regularization of gradient image in low frequency is used to suppress the limited-angle artifacts, to preserve the edge of object and to smooth the reconstructed image. To solve the proposed model, a proximal alternating linearized Peaceman–Rachford splitting method (PAL-PRSM) is proposed, which uses the Peaceman–Rachford splitting method that updates the Lagrange multiplier twice, one after each minimization of the subproblem, to deal with the optimization problem firstly, and then the proximal linearization is used to avoid computing the inverse of a huge system matrix. In addition, to compensate the proximal linearization, we add an additional term into Lagrange multiplier updating. Real data experiments are investigated to demonstrate the effectiveness of PAL-PRSM method, and the results show that the proposed method outperforms two other CT reconstruction methods on preserving the edge of reconstructed image. On the whole, the proposed method is a compromise between denoising and preserving the edge of reconstructed image.