A fast iterative soft-threshold algorithm for few-view CT reconstruction

A fast iterative soft-threshold algorithm is proposed to accelerate the convergence of iterative soft-threshold algorithm for image reconstruction from few-view projections. The algorithm bases on total variation minimization. Simultaneous algebraic reconstruction technique (SART) is used to reconstruct image from few-view projections and to meet the constraint of the projection data. Then discrete gradient transform (DGT) of the reconstructed image is calculated and the soft-threshold filtering is performed on the DGT. Finally the reconstructed image is updated using the pseudo-inverse of the DGT. The proposed algorithm takes the images in previous two iterations as the input image for a new iteration, and hence the convergence is accelerated. Experimental results and comparisons with the SART algorithm, the fast iterative soft-threshold algorithm with Harr wavelet constraint, and the iterative soft-threshold filtering algorithm with total variation constraint on the projections of Shepp-Logan phantom under the conditions without noise and corrupted by Poisson noise assuming with 5×10⁴ and 2×10⁵ photons per detector element show that the proposed algorithm can not only speed up the convergence, but also reduce the relative reconstruction error of images.