Image Reconstruction Using a Mixture Score Function (MSF).

Computed tomography (CT) reconstructs volumetric images using X-ray projection data acquired from multiple angles around an object. For low-dose or sparse-view CT scans, the classic image reconstruction algorithms often produce severe noise and artifacts. To address this issue, we develop a novel iterative image reconstruction method based on maximum a posteriori (MAP) estimation. In the MAP framework, the score function, i.e., the gradient of the logarithmic probability density distribution, plays a crucial role as an image prior in the iterative image reconstruction process. By leveraging the Gaussian mixture model, we derive a novel score matching formula to establish an advanced score function (ADSF) through deep learning. Integrating the new ADSF into the image reconstruction process, a new ADSF iterative reconstruction method is developed to improve image reconstruction quality. The convergence of the ADSF iterative reconstruction algorithm is proven through mathematical analysis. The performance of the ADSF reconstruction method is also evaluated on both public medical image datasets and clinical raw CT datasets. Our results show that the ADSF reconstruction method can achieve better denoising and deblurring effects than the state-of-the-art reconstruction methods, showing excellent generalizability and stability.