{"ID":5554327,"CreatedAt":"2026-07-02T02:11:27.934456424Z","UpdatedAt":"2026-07-04T17:06:47.734863441Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.01176","arxiv_id":"2607.01176","title":"High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction","abstract":"Magnetic resonance imaging (MRI) reconstruction under realistic acquisition conditions can be fundamentally viewed as estimating the underlying k-space distribution from incomplete and noise-corrupted measurements. While diffusion models have recently shown strong potential as generative prior for inverse problems,existingapproachesstruggletohandlenoisyreconstruction settings, especially when operating directly in k-space domain. In this work, we propose a unified high-dimensional k-space reconstruction framework tailored for noisy inverse problems, whichenhancesdiffusion-based solversthroughrepresentation lifting.Ratherthanmodifyingthe underlying optimization procedures, the proposed framework augments the data representation space, enabling existing diffusion-based solvers to operate on enriched k-space embeddings with improved expressiveness. Extensive experiments on both in-house and public datasets across varying noise levels and undersampled factors demonstrate that the proposed frame work consistently improves reconstruction quality for multiple diffusion-based inverse solvers. Notably, the largest gains are observed in high-noise regimes, which is consistent with our theoretical analysis of error propagation under high-dimensional representation. These results suggest that high-dimensional representation provides a general and model-agnostic mechanism for improving diffusion-based MRI reconstruction in noisy settings, offering a new perspective on robust k-space generative modeling for practical inverse problems. The code will be available at https://github.com/yqx7150/HEP-MRIRec.","short_abstract":"Magnetic resonance imaging (MRI) reconstruction under realistic acquisition conditions can be fundamentally viewed as estimating the underlying k-space distribution from incomplete and noise-corrupted measurements. While diffusion models have recently shown strong potential as generative prior for inverse problems,exis...","url_abs":"https://arxiv.org/abs/2607.01176","url_pdf":"https://arxiv.org/pdf/2607.01176v1","authors":"[\"Yu Guan\",\"Tianjia Huang\",\"Qinrong Cai\",\"Qiuyun Fan\",\"Dong Liang\",\"Qiegen Liu\"]","published":"2026-07-01T17:08:17Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[\"Diffusion Model\"]","has_code":false,"code_links":[{"ID":613871,"CreatedAt":"2026-07-02T02:11:27.934456424Z","UpdatedAt":"2026-07-02T02:11:27.934456424Z","DeletedAt":null,"paper_id":5554327,"paper_url":"https://arxiv.org/abs/2607.01176","paper_title":"High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction","repo_url":"https://github.com/yqx7150/HEP-MRIRec","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}