A novel weighted total difference based image reconstruction algorithm for few-view computed tomography

In practical applications of computed tomography (CT) imaging, due to the risk of high radiation dose imposed on the patients, it is desired that high quality CT images can be accurately reconstructed from limited projection data. While with limited projections, the images reconstructed often suffer severe artifacts and the edges of the objects are blurred. In recent years, the compressed sensing based reconstruction algorithm has attracted major attention for CT reconstruction from a limited number of projections. In this paper, to eliminate the streak artifacts and preserve the edge structure information of the object, we present a novel iterative reconstruction algorithm based on weighted total difference (WTD) minimization, and demonstrate the superior performance of this algorithm. The WTD measure enforces both the sparsity and the directional continuity in the gradient domain, while the conventional total difference (TD) measure simply enforces the gradient sparsity horizontally and vertically. To solve our WTD-based few-view CT reconstruction model, we use the soft-threshold filtering approach. Numerical experiments are performed to validate the efficiency and the feasibility of our algorithm. For a typical slice of FORBILD head phantom, using 40 projections in the experiments, our algorithm outperforms the TD-based algorithm with more than 60% gains in terms of the root-mean-square error (RMSE), normalized root mean square distance (NRMSD) and normalized mean absolute distance (NMAD) measures and with more than 10% gains in terms of the peak signal-to-noise ratio (PSNR) measure. While for the experiments of noisy projections, our algorithm outperforms the TD-based algorithm with more than 15% gains in terms of the RMSE, NRMSD and NMAD measures and with more than 4% gains in terms of the PSNR measure. The experimental results indicate that our algorithm achieves better performance in terms of suppressing streak artifacts and preserving the edge structure information of the object.