Iterative CT reconstruction via minimizing adaptively reweighted total variation

Abstract

Iterative reconstruction via total variation (TV) minimization has demonstrated great successes in accurate CT imaging from under-sampled projections. When projections are further reduced, over-smoothing artifacts appear in the current reconstruction especially around the structure boundaries. We propose a practical algorithm to improve TV-minimization based CT reconstruction on very few projection data. Based on the theory of compressed sensing, the L-0 norm approach is more desirable to further reduce the projection views. To overcome the computational difficulty of the non-convex optimization of the L-0 norm, we implement an adaptive weighting scheme to approximate the solution via a series of TV minimizations for practical use in CT reconstruction. The weight on TV is initialized as uniform ones, and is automatically changed based on the gradient of the reconstructed image from the previous iteration. The iteration stops when a small difference between the weighted TV values is observed on two consecutive reconstructed images. We evaluate the proposed algorithm on both a digital phantom and a physical phantom. Using 20 equiangular projections, our method reduces reconstruction errors in the conventional TV minimization by a factor of more than 5, with improved spatial resolution. By adaptively reweighting TV in iterative CT reconstruction, we successfully further reduce the projection number for the same or better image quality.