基于超复数的高保真磁共振波谱重建

Magnetic Resonance Spectroscopy (MRS) can determine the chemical or physical state of atoms. MRS is an important biomedical detection method which is widely used in the analysis of bio-molecular structures and non-invasive detection of metabolites in living tissues. The acquisition time of MRS grows sharply with the increase of signal dimension. Non-uniform sampling is the forerunner of fast MRS, and how to reconstruct spectra with high fidelity from insufficient data is the core issue. By exploiting the hypercomplex and exponential signal characteristics of multidimensional MRS, this project aims to establish hypercomplex low rank Hankel matrix/tensor reconstruction models and fast numerical algorithms, and solve the challenging MRS reconstructions with dense spectral peak, large dynamic range or low sampling rate. The proposed methods will be tested in biomedical applications with quantitative assessment. The success of this project will promote the development of multidimensional hypercomplex spectral reconstruction theory and boost the interdisciplinary applications of high-resolution fast MRS in the fields of biology, medicine and chemistry.

磁共振波谱（Magnetic Resonance Spectroscopy，MRS）能测定原子的化学或物理状态，广泛用于解析生物分子结构和无创检测活体组织代谢产物等，是重要的生物医学检测方法。MRS采集时间随信号维度增加而急剧增长，非均匀采样是快速MRS的前沿方法，如何从不足数据中高保真重建多维谱是其面临的核心问题。本项目利用多维MRS的超复数和指数信号特点，建立基于超复数的低秩Hankel矩阵/张量的重建模型与快速数值算法，致力于解决密集谱峰、大动态范围和低采样率等挑战性的多维MRS重建问题，并进行生物医学应用和量化评估。本项目的开展将促进多维超复数谱重建理论发展，推动高分辨率快速MRS在生物、医学和化学等领域的交叉学科应用。

本项目主要利用多维磁共振谱的超复数和指数信号特点，建立基于超复数的低秩Hankel矩阵/张量的重建模型与快速数值算法，解决了低强度谱峰和低采样率等挑战性的多维MRS重建问题，并进行生物医学应用和量化评估等。此外，相关方法还被扩展到磁共振成像的快速重建中。.在项目基金支持下，共计发表 20篇 SCI 期刊论文，其中一区/TOP 期刊论文 6 篇、二区期刊论文5篇、三区/四区论文 9篇。发表的期刊包括Signal Processing (SCI, JCR 2, IF 4.72)、 Journal of Magnetic Resonance (SCI, JCR 3, IF 2.73)、IEEE Transactions on Neural Networks and Learning Systems（SCI, JCR 1, IF 14.25）等研究领域内知名期刊与 Angewandte Chemie International Edition (TOP Journal, JCR 1,IF 16.82）等交叉学科顶级期刊；并申请中国发明专利2项（已授权1项），所取得成果远超预期目标。