A novel fast spectral computed tomography reconstruction method with spectral windowed analytical iterative technique

Spectral X-ray computed tomography (SCT) has been widely applied in both industrial non-destructive testing and medical diagnosis. SCT reconstruction can be summarized as solving ill-conditioned large sparse nonlinear systems. This work aims to develop a spectral windowed analytical iterative technique (SWAIT) for SCT reconstruction, enhancing both image quality and reconstruction efficiency. A special window function is derived mathematically, and it varies with the number of iterations, X-ray spectrum, basis material images and mass attenuation coefficients. The window function follows the frequency principle "from low to high", and the dynamic window function can achieve global minimizers. Simulation and real data experiments validate that the proposed method converges quickly, retains effective high-frequency information, suppresses noise, and reduces the propagation of decomposition errors in the image domain. The results demonstrate that the electron density errors of reconstructed water are less than 5%, and those of PET and glass are less than 3%, which shows significant practical potential.