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Spectral computed tomography (spectral CT) is a promising medical imaging technology because of its ability to provide information on material characterization and quantification. However, with an increasing number of basis materials, the nonlinearity of measurements causes difficulty in decomposition. In addition, noise amplification and beam hardening further reduce image quality. Thus, improving the accuracy of material decomposition while suppressing noise is pivotal for spectral CT imaging. This paper proposes a one-step multi-material reconstruction model as well as an iterative proximal adaptive decent method. In this approach, a proximal step and a descent step with adaptive step size are designed under the forward–backward splitting framework. The convergence analysis of the algorithm is further discussed according to the convexity of the optimization objective function. For simulation experiments with different noise levels, the peak signal-to-noise ratio (PSNR) obtained by the proposed method increases approximately 23 dB, 14 dB, and 4 dB compared to those of other algorithms. Magnified areas of thorax data further demonstrated that the proposed method has a better ability to preserve details in tissues, bones, and lungs. Numerical experiments verify that the proposed method efficiently reconstructed the material maps, and reduced noise and beam hardening artifacts compared with the state-of-the-art methods.

Limited-angle computed tomography (CT) image reconstruction is a challenging problem in the field of CT imaging. In some special applications, limited by the geometric space and mechanical structure of the imaging system, projections can only be collected with a scanning range of less than 90°. We call this kind of serious limited-angle problem the ultra-limited-angle problem, which is difficult to effectively alleviate by traditional iterative reconstruction algorithms. With the development of deep learning, the generative adversarial network (GAN) performs well in image inpainting tasks and can add effective image information to restore missing parts of an image. In this study, given the characteristic of GAN to generate missing information, the sinogram-inpainting-GAN (SI-GAN) is proposed to restore missing sinogram data to suppress the singularity of the truncated sinogram for ultra-limited-angle reconstruction. We propose the U-Net generator and patch-design discriminator in SI-GAN to make the network suitable for standard medical CT images. Furthermore, we propose a joint projection domain and image domain loss function, in which the weighted image domain loss can be added by the back-projection operation. Then, by inputting a paired limited-angle/180° sinogram into the network for training, we can obtain the trained model, which has extracted the continuity feature of sinogram data. Finally, the classic CT reconstruction method is used to reconstruct the images after obtaining the estimated sinograms. The simulation studies and actual data experiments indicate that the proposed method performed well to reduce the serious artifacts caused by ultra-limited-angle scanning.