Implicit neural prior‐guided diffusion for spectral CT reconstruction

Abstract Background Spectral computed tomography (CT) plays a crucial role in various fields. However, the cumulative radiation dose from repeated x‐ray CT examinations has raised concerns about potential health risks. Reducing the projection view is an effective strategy to reduce the radiation dose, but this will lead to a notable degradation in image quality, resulting in streaking artifacts. Purpose This work aims to develop a novel spectral CT reconstruction method to alleviate the ill‐posed nature of the sparse sampling image reconstruction, while suppressing streaking artifacts and recovering detailed structures. Methods In the scope of this work, we propose an implicit neural representation (INR) prior‐guided diffusion (NeRDiff) method for spectral CT reconstruction, effectively combining the capabilities of implicit prior representation of INR and detail recovery of score‐based generative models (SGM). NeRDiff includes two key designed phases: gradient‐penalized INR learning and Pos‐INR guided SGM reconstruction. In the first phase, an improved INR is devised and utilized to enhance the network's ability of representing complex signals by applying the variable‐periodic activation function in multilayer perception network and adopting a dual‐domain loss function. In the second phase, the INR prior is incorporated as a prior guiding Langevin dynamics sampling in the reverse diffusion process of SGM. In addition, a unified mathematical model and an efficient algorithm are proposed to enhance reconstruction stability. Results Quantitative and qualitative assessments on ultra‐sparse‐view datasets from numerical simulation and preclinical mouse underscore the superiority of NeRDiff over alternative methods. Especially in the simulation experiment, the NeRDiff method achieves improvement of at least 4.75 and 1.70 dB in PSNR under 20‐view compared to the SGM proposed by Song et al. (Song‐CT) and the wavelet‐improved score‐based generative model (WSGM). Conclusions In this work, we propose the NeRDiff method for highly ill‐defined spectral CT reconstruction tasks. We have conducted a series of experiments in the ultra‐sparse‐view reconstruction task, and the experimental results consistently demonstrate the remarkable capabilities of NeRDiff in terms of anti‐artifact performance and detail preservation.