融合局部低秩先验与Bloch流形约束的磁共振指纹重建算法

Local Low-Rank and Bloch Manifold Regularized Magnetic Resonance Fingerprinting Reconstruction

为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间数据存在大量的混叠伪影,直接影响到组织生理参数的重建准确度.为此需要将各种先验知识引入重建模型之中,以缓解MRF重建问题的不适定性.针对上述问题,本文提出一种融合局部低秩先验与Bloch流形约束的MRF重建模型,并使用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解模型中的非凸MRF重建问题.本文算法在引入MRF像空间数据的局部低秩先验的同时,使用预先构建的字典为重建指纹提供流形约束.一方面通过空域局部低秩约束有效抑制混叠伪影的产生,另一方面利用字典先验避免指纹的时域流形特征在迭代重建过程中丢失.仿真实验结果表明,相较于引入了全局低秩先验与Bloch流形约束的其他同类算法,本文算法可以提供更高的组织参数重建准确度.

To reduce the scanning time,magnetic resonance fingerprinting(MRF)generally performs non-Cartesian sparse undersampling in the K-space.However,it's an ill-posed problem to reconstruct MRF data from the sparse K-space data.There are severe artifacts in the reconstructed MRF data,which subsequently reduce the reconstruction accuracy of the tissue parameters.So,it's necessary to utilize a variety of prior knowledge to alleviate the ill-posed nature of the MRF reconstruction problem.For this purpose,we propose a new MRF reconstruction model in which the local low-rank prior and the Bloch manifold constraints are combined to help recovering MRF data from its highly undersampled K-space data,and utilize the alternating direction method of multipliers(ADMM)algorithm to solve the corresponding non-convex MRF reconstruction problem.On the one hand,the local low-rank prior has powerful de-redundancy capability that can remove aliasing artifacts.On the other hand,the MRF dictionary,which is predefined using Bloch equation,can provide fingerprint prior for each foreseeable physiological tissue,so as to regularize the temporal manifold features of the reconstructed fingerprints.The results of the simulation experiments show that,compared with the other iterative methods which integrate the global low-rank prior and the Bloch manifold constraints,the proposed method has better performance on the reconstruction accuracy of multiple tissue physiological parameters.