Nonlocal Tensor Decomposition With Joint Low Rankness and Smoothness for Spectral CT Image Reconstruction

Spectral computed tomography (CT) is a medical imaging technology that utilizes the measurement of X-ray energy absorption in human tissue to obtain image information. It can provide more accurate and detailed image information, thereby improving the accuracy of diagnosis. However, the process of spectral CT imaging is usually accompanied by a large amount of radiation and noise, which makes it difficult to obtain high-quality spectral CT image. Therefore, this paper constructs a basic third-order tensor unit based on the self-similarity of patches in the spatial domain and spectral domain while proposing nonlocal spectral CT image reconstruction methods to obtain high-quality spectral CT image. Specifically, the algorithm decomposes the recombination tensor into a low-rank tensor and a sparse tensor, which are applied by weighted tensor nuclear norm (WTNN) and weighted tensor total variation (WTTV) norm to improve the reconstruction quality, respectively. In order to further improve algorithm performance, this paper also uses weighted tensor correlated total variation regularization(WTCTV) to simultaneously characterize the low rankness and smoothness of low-rank tensor, while the sparse tensor uses weighted tensor total variation regularization (WTTV) to represent the piecewise smooth structure of the spatial domain and the similarity between pixels and adjacent frames in the spectral domain. Hence, the proposed models can effectively provide faithful underlying information of spectral CT image while maintaining spatial structure. In addition, this paper uses the Alternating Direction Method of Multipliers(ADMM) to optimize the proposed spectral CT image reconstruction models. To verify the performance of the proposed algorithms, we conducted a large number of experiments on numerical phantom and clinic patient data. The experimental results indicate that incorporating weighted regularization outperforms the results without weighted regularization, and nonlocal similarity can achieve better results than that without nonlocal similarity. Compared with existing popular algorithms, the proposed models significantly reduce running time and improve the quality of spectral CT image, thereby assisting doctors in more accurate diagnosis and treatment of diseases.