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. •We propose a method for enhancing MR image quality by reducing artifacts and noise simultaneously. Motivated by the properties of these undesired components, our method combines the advantages of both k-space and image space to enhance images.•We construct the discrete shape space of images (DSSI) to measure the intrinsic image similarity in Riemannian manifold by treating images as shapes from a geometric view. Therefore, image similarity is independent of similarity transformations.•The patch-based rank-ordered difference (PROD) is defined under the framework of the DSSI to detect and remove MR artifacts in k-space. The PROD is defined by a signed distance between patches as artifacts usually appear as sparse outliers with prominent features.•We design an improved filter using the similarity function of images defined in the DSSI to reduce noise in the image space. This is an interesting advantage when compared with the similarity function used in the classical NLM, which is rather sensitive to rotation.•We theoretically investigate the convergence of our improved filter and find that using the geometric information of images to measure the similarity between images can ensure that the restored image is an effective estimator of the ideal image.