Total variation combining nonlocal means filtration for image reconstruction in X-ray computed tomography.

Background: Image reconstruction for realistic medical images under incomplete observation is still one of the core tasks for computed tomography (CT). However, the stair-case artifacts of Total variation (TV) based ones have restricted the usage of the reconstructed images.

Objective: This work aims to propose and test an accurate and efficient algorithm to improve reconstruction quality under the idea of synergy between local and nonlocal regularizations.

Methods: The total variation combining the nonlocal means filtration is proposed and the alternating direction method of multipliers is utilized to develop an efficient algorithm. The first order approximation of linear expansion at intermediate point is applied to overcome the computation of the huge CT system matrix.

Results: The proposed method improves root mean squared error by 25.6% compared to the recent block-matching sparsity regularization (BMSR) on simulation dataset of 19 views. The structure similarities of image of the new method is higher than 0.95, while that of BMSR is about 0.92. Moreover, on real rabbit dataset of 20 views, the peak signal-to-noise ratio (PSNR) of the new method is 36.84, while using other methods PSNR are lower than 35.81.

Conclusions: The proposed method shows advantages on noise suppression and detail preservations over the competing algorithms used in CT image reconstruction.