Solving inverse problem via latent variable optimization of diffusion models: An application to CT reconstruction

Inverse problems are widely studied in various scientific fields, including mathematics, physics, and medical imaging (such as CT and MRI reconstructions). In this talk, I will present a novel method for solving inverse problems using the diffusion model, with an application to CT reconstruction. The diffusion model, which is a core component of recent image-generative AI, such as Stable Diffusion and DALL-E3, is capable of producing high-quality images with rich diversity. The imaging process in CT (i.e., CT reconstruction) is mathematically an inverse problem. When the radiation dose is reduced to minimize a patient's exposure, image quality deteriorates due to information loss, making the CT reconstruction problem highly ill-posed. In the proposed method, the diffusion model, trained with a large dataset of high-quality images, serves as a regularization technique to address the ill-posedness. Consequently, the proposed method reconstructs high-quality images from sparse (low-dose) CT data while preserving the patient's anatomical structures. We also compare the performance of the proposed method with those of other existing methods, and find that the proposed method outperforms the existing methods in terms of quantitative indices.