基于低秩Hankel矩阵的快速高维磁共振波谱重建

High dimensional magnetic resonance spectroscopy (MRS) can measure the molecular structure and provide fruitful information. It has been widely applied in medical imaging, chemistry and biology, etc. However, the data acquisition time increases exponentially with the number of dimensions, which prevents MRS goes into time-consuming applications that can unfold more complex molecular structures. Non-uniformly sampling (NUS) accelerates the data acquisition by undersampling the signal and then reconstructs the spectroscopy by solving under-determined problems. How to reconstruct high quality spectra from non-uniformly sampled data is challenging and a hot topic in the field of MRS. This project explores a general property that the time-domain signal of MRS can be approximated by a sum of exponentials and its Hankel matrix is low rank if the number of spectral peaks is much smaller than the length of time-domain signal. Research work in the project will be conducted as follows: a) Construct the low rank Hankel matrix for high dimensional MRS and develop low-complexity reconstruction algorithms; b) Derive theoretical bounds of Hankel low rank recovery for non-uniformly sampled MRS; c) Propose prior knowledge-assisted NUS schemes and spectral reconstruction methods; d) Improve the spectra quality by combing other state-of-art fast MRS techniques, e.g. compressed sensing and single-scan methods. It is expected that this project will lead to new theories, methods and algorithms for low-rank Hankel matrix based NUS MRS, and improve fast MRS techniques, enabling more important applications in the interdiscipline.

高维磁共振波谱能测定分子结构并提供丰富信息，广泛应用在医学、化学和生物学等领域。但数据采集时间随维度增加而指数级增长，这极大地限制高维磁共振波谱的应用。非均匀采样通过欠采样信号加速波谱采集，从不足的数据中恢复出完整的谱是一个欠定方程求解问题。如何从欠采样数据中重建高质量波谱是磁共振领域的前沿和热点问题之一。本项目将磁共振波谱的时域信号构建成Hankel矩阵，利用谱峰个数远小于信号长度时的矩阵低秩特性进行谱重建。研究内容包括：1）构建高维谱的低秩Hankel矩阵模型和低复杂度重建算法；2）推导低秩Hankel矩阵重建磁共振波谱的理论条件；3）提出基于先验知识的增强型非均匀采样和谱重建方法；4）结合压缩感知和单扫描等快速信号采集方法来提高波谱重建质量。本项目拟建立一套基于低秩Hankel矩阵的高维磁共振波谱非均匀采样的理论、模型和算法，促进快速磁共振技术的发展及其在交叉学科的应用。

为了解决高维磁共振波谱的快速采样和高保真重建问题，项目主要在磁共振波谱中开展了基于低秩Hankel矩阵和人工智能的MRS谱重建等一系列原创方法研究，提出了从一维到任意高维的MRS低秩Hankel重建方法，首次提出人工智能MRS方法快速重建以达到秒级重建，扩展相关方法到磁共振成像等。. 在项目基金支持下，共计发表15篇SCI期刊论文，一区/TOP期刊论文6篇、二区期刊论文6篇、三区/四区论文3篇。其中2篇论文入选ESI高引(3%)，发表的期刊包括IEEE Trans. Signal Processing (TOP, JCR 2, IF 5.23)、IEEE Trans. Medical Imaging (TOP，JCR 2, IF 7.82)、IEEE Trans. Biomedical Engineering(JCR 2, IF 4.49 )等信号处理、医学成像顶级期刊和Angewandte Chemie International Edition (TOP Journal, JCR 1, IF 12.26）等交叉学科顶级期刊；并申请中国发明专利9项（已授权7项）和PCT专利1项，所取得成果远超预期目标。