Joint magnetic resonance imaging artifacts and noise reduction on discrete shape space of images

Magnetic resonance (MR) images can be corrupted by artifacts and noise, potentially leading to misinterpretation of the images. In this paper, we propose a novel approach based on the discrete shape space of images (DSSI) to jointly reduce artifacts and noise in MR images. The proposed method restores MR images in multiple domains based on the distinct generation mechanisms of noise and artifacts. The images in multiple domains are analyzed in a non-Euclidean space. The DSSI is constructed as a Riemannian manifold to measure the intrinsic properties of images. Images are considered shapes from a geometric perspective, and the impact of similarity transformations (e.g., rotation, scaling, and translation) on image analysis is eliminated. The patch-based rank-ordered difference (PROD) detector is defined in k-space within the framework of DSSI to detect and remove sparse outliers that cause artifacts. In addition, a novel similarity function for images is defined using the DSSI and be used to design the improved filter. Finally, the convergence of the improved filter is theoretically analyzed, indicating that our method offers an effective estimator of the ideal image. The experimental results of various MR images demonstrate that the proposed approach outperforms classical and state-of-the-art methods for artifact correction and noise removal, both qualitatively and quantitatively.