Low-complexity reconstruction of low-dose spectral CT via double low-rank tensor factorization with adaptive...

Spectral computed tomography (CT) is a medical imaging technology that provides doctors with more detailed and accurate imaging information by synchronously collecting multi-energy X-ray data and analyzing the absorption characteristics of matter in different energy ranges. However, insufficient photon counts in each energy bin can cause significant noise in the reconstructed image, especially under low-dose conditions. This paper proposes a sparse-view spectral CT reconstruction method based on spatial factors denoising within a double low-rank tensor factorization framework. This method effectively suppresses mixed noise and reduces computational complexity by fully mining global spectral low-rankness, group sparsity, and nonlocal self-similarity. Specifically, this paper employs double low-rank tensor factorization to model the global low-rank structure inherent in spectral CT images. To fully exploit nonlocal self-similarity within the spatial factor across both spatial and spectral dimensions, we construct third-order tensor patches and enhance their low-rankness by introducing the weighted tensor nuclear norm constraint. Concurrently, to promote shared structural information, we apply weighted group sparsity constraints to the spatial gradients of spatial factor. Hence, the proposed model can faithfully characterize the real underlying structure of spectral CT image by cleverly combining global, nonlocal and local prior information. Moreover, we use the proximal alternating minimization algorithm to solve the proposed model and provide a theoretical guarantee for its convergence. Extensive numerical simulations and clinical patient data experiments demonstrate that the proposed method for low-dose spectral CT reconstruction exhibits significant advantages in reducing computational complexity and improving spectral CT image quality compared to existing popular algorithms.