Robust Frame Based X-Ray CT Reconstruction (Journal of Computational Mathematics, 2021)
As X-ray computed tomography (CT) is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this purpose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the interior tomography scheme which only illuminates a region-of-interest (ROI), one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three different parts: cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART+TV methods in terms of preservation of sharp edges, mean structural similarity (SSIM), contrast-to-noise ratio, relative error and correlations. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART+TV methods need more than 200 projections. Additionally, the proposed robust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART+TV methods.
Keywords: Computed tomography; Wavelet frame; Split Bregman algorithm.