Weighted Tensor Low-Rankness and Learnable Analysis Sparse Representation Model for Texture Preserving Low-Dose CT Reconstruction

In CT images, tissue structures and lesion changes illustrate evident non-local self-similarity and regionally constant properties. The low-rank model and the learnable sparse representation model are powerful tools that can respectively encode the correlations among non-local similar patches and the sparsity in a local transformed subspace about the underlying CT image. Existing Model-Based Iterative Reconstruction (MBIR) methods generally adopt one of the two models alone for CT reconstruction, which might suffer from modelling deficiency and hampers their reconstruction performance. In this study, we presented a novel Weighted Tensor Low-Rank and Learnable Analysis Sparse Representation model (WTLR-LASR) to simultaneously encode the non-local correlations and local transformed sparsity natures. Specifically, we developed a novel Weighted Tensor Nuclear Norm Minimization (WTNNM) formulation to characterize the weighted tensor low-rank model, and introduced the Weighted Tensor Nuclear Norm Proximal (WTNNP) operator to solve the non-convex WTNNM problem. We further proved that the WTNNP problem can be equivalently transformed to a weighted matrix nuclear norm proximal (WMNNP) problem in the Fourier transform domain, which allowed us to easily reach the closed-form optimum of the WTNNP problem. We proposed a novel CT reconstruction algorithm based on the presented WTLR-LASR model. We also introduced a genetic algorithm to automatically select the parameters in the proposed algorithm. Extensive experimental studies were performed to validate the effectiveness of the proposed algorithm. The results demonstrate that the proposed algorithm can achieve noticeable improvements over state-of-the-art methods in terms of noise suppression and textures preservation.