Enhancing photon-counting computed tomography reconstruction via subspace dictionary learning and spatial sparsity regularization.

Background: Photon-counting computed tomography (CT) is an advanced imaging technique that enables multi-energy imaging from a single scan. However, the limited photon count assigned to narrow energy bins leads to increased quantum noise in the reconstructed spectral images. To address this issue, leveraging the prior information in the spectral images is essential. This study aimed to develop an efficient algorithm that enhances image reconstruction quality by reducing noise levels and preserving image details. Methods: To improve image reconstruction quality for photon-counting CT, we propose an algorithm based on the subspace-assisted multi-prior information, including global, nonlocal, and local priors, for spectral CT reconstruction. Specifically, the algorithm first maps spectral CT images, which exhibit global low-rank characteristics, to low-dimensional eigenimages using subspace decomposition. Then, similar image patches are extracted based on the manifold structure distance from highly correlated eigenimages in both spectral and spatial domains. These patches are stacked to form a nonlocal full-channel tensor group. Subsequently, non-convex structural sparsity is applied to this tensor group through adaptive dictionary learning, exploiting nonlocal similarity. Finally, the alternating direction method of multipliers (ADMM) is applied to solve the optimization model iteratively. Results: The simulated walnut and real mouse data were applied to validate the effectiveness of the proposed method. In the simulation experiments, the proposed method reduced the root mean square error (RMSE) by 87.74%, 86.88%, 67.01%, 46.42%, and 13.51% compared to the respective state-of-the-art five comparison methods. The time taken for one iteration of the proposed algorithm was as low as 32.57 seconds, which was 92.07% less than framelet tensor nuclear norm [framelet tensor sparsity with block-matching method (FTNN)] method and 74.13% less than total variation regularization [tensor nonlocal similarity and local TV sparsity method (ITS_TV)] method, the other two tensor block-matching (BM)-based comparison methods. The material decomposition results in real mouse data further validated the accuracy of the proposed method for different materials. Conclusions: The experimental results indicate that the proposed algorithm effectively reduces computational costs while improving the accuracy of image reconstruction and material decomposition, showing promising advantages over the compared method.