Convergence of NADA-HT algorithm for CT image reconstruction

One of the main advantages of the widely applied -norm minimization is the great reduction in streak artifacts for computed tomography image reconstruction with limited-angle projections. However, the results are over smoothing, not sparse enough and lack of some details, causing edge blurred. To address these issues, we proposed a combined -norm and -norm regularization model and developed the NADA-HT algorithm to solve the optimization effectively using the nonmonotone alternating direction algorithm with a hard thresholding. In this paper, the convergence of the algorithm is analyzed and the weights between the -norm and -norm terms in the model are discussed. A lower bound of decrements of the objective function is derived in terms of the difference of the reconstructed images for sufficiently large iteration numbers under certain conditions. It is further shown that there exists a subsequence of the reconstructed image sequence converging to a local minimizer. Numerical experiments demonstrate the reconstruction results by using different weights of the -norm term and lead to discussions on parameter selection.