3D ring artifacts removal algorithm combined low‐rank tensor decomposition with spatial–sequential total variation regularization and its application in phase‐contrast microtomography

High-resolution synchrotron radiation X-ray phase contrast microtomography (PC-μCT) images often suffer from severe ring artifacts, which are mainly caused by undesirable responses of detector elements. In the medical imaging field, the existence of ring artifacts can lead to degraded visual quality and can directly affect diagnosis accuracy. Thus, removing or at least effectively reducing ring artifacts is indispensable.The existing ring artifacts removal algorithms mainly focus on two-dimensional (matrix-based) priors, and these algorithms fail to consider correlations hidden in sequential computed tomography (CT) images. This paper proposed a novel three-dimensional (tensor-based) ring artifacts removal algorithm for synchrotron radiation X-ray PC-μCT images. In the sinogram domain, ring artifacts manifest as vertical stripe artifacts. From an image decomposition perspective, a degraded sinogram can be decomposed into a stripe artifacts component and an underlying clean sinogram component. The proposed algorithm is designed to detect and remove stripe artifacts from a degraded sinogram by fully identifying the characteristics of the two components. Specifically, for the stripe artifacts component, tensor Tucker decomposition is used to describe its low-rank character. For the underlying clean sinogram component, spatial-sequential total variation regularization is adopted to enhance the piecewise smoothness. Moreover, the Frobenius norm term is further used to model Gaussian noise. An efficient augmented Lagrange multiplier method is designed to solve the proposed optimization model.The proposed method is evaluated utilizing both simulations and real data containing different ring artifacts patterns. In the simulations, the human chest CT images are used for evaluating the proposed method. We compare the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and mean absolute error (MAE) results of our algorithm with the Naghia's method, the RRRTV method, the wavelet-FFT method, and the SDRSD-GIF method. The proposed method was also evaluated on real data from rat liver samples and rat tooth samples. Our proposed method outperforms the competing methods in terms of both qualitative and quantitative evaluation results. Additionally, the 3D visualization results were presented to make the ring artifacts removal effect more intuitive.The experimental results on simulations and real data clearly demonstrated that the proposed algorithm can significantly improve the quality of PC-μCT images compared with the existing popular algorithms, and it has great potential to promote the application of high-resolution imaging for visualizing biological tissues.