Low-dose computed tomography image reconstruction from under-sampling data based on weighted total variation minimization

This paper introduced a novel method to reconstruct low-dose computed tomography (LDCT) images based on weighted total variation minimization. Previous work has shown that a CT image can be reconstructed from under-sampling data by minimizing the total variation (TV) of the image with some constraints. However, due to the piecewise constant assumption, the conventional TV minimization algorithm often suffers over-smooth on the edges of the resulted image. Considering the anisotropic property of the edge voxels in an image, we proposed a weighted total variation (WTV) minimization algorithm to achieve high-quality LDCT image reconstruction from under-sampling sinogram data. The proposed algorithm was evaluated by computer simulation, where the Shepp-Logan phantom was used. In noise free cases, 20 projection views were enough to accurately reconstruct the phantom image by the WTV approach while the filtered backprojection (FBP) reconstruction failed. In noise cases, different levels of Poisson noise were added to the noise-free sinogram. The local signal to noise ratio (SNR) and global SNR were computed to evaluate the robustness of the WTV algorithm to the noise. The simulation results showed that the WTV algorithm can have much higher global SNR compared to the conventional TV. The relationship between the number of views of WTV algorithm and the mean square error (MSE) of the reconstructed images was also discussed in this paper in order to find the minimum projection numbers required to obtain an adequate reconstruction image for low-dose CT applications.