  Image generative AI has garnered significant attention in recent years. In
particular, the diffusion model, a core component of recent generative AI,
produces high-quality images with rich diversity. In this study, we propose a
novel CT reconstruction method by combining the denoising diffusion
probabilistic model with iterative CT reconstruction. In sharp contrast to
previous studies, we optimize the fidelity loss of CT reconstruction with
respect to the latent variable of the diffusion model, instead of the image and
model parameters. To suppress anatomical structure changes produced by the
diffusion model, we shallow the diffusion and reverse processes, and fix a set
of added noises in the reverse process to make it deterministic during
inference. We demonstrate the effectiveness of the proposed method through
sparse view CT reconstruction of 1/10 view projection data. Despite the
simplicity of the implementation, the proposed method shows the capability of
reconstructing high-quality images while preserving the patient's anatomical
structure, and outperforms existing methods including iterative reconstruction,
iterative reconstruction with total variation, and the diffusion model alone in
terms of quantitative indices such as SSIM and PSNR. We also explore further
sparse view CT using 1/20 view projection data with the same trained diffusion
model. As the number of iterations increases, image quality improvement
comparable to that of 1/10 sparse view CT reconstruction is achieved. In
principle, the proposed method can be widely applied not only to CT but also to
other imaging modalities such as MRI, PET, and SPECT.
