基于调和误差去除的定量磁敏感率成像重建

Quantitative susceptibility mapping (QSM) aims to visualize the three-dimensional susceptibility distribution by solving the field-to-source inverse problem using the phase data in magnetic resonance signal. However, the inverse problem is ill-posed since the Fourier transform of integral kernel has zeroes in the frequency domain. Although numerous regularization based models have been proposed to overcome this problem, the incompatibility in the field data, which leads to deterioration of the recovery, has not received enough attention. In our recent work, we have shown that the data acquisition process of QSM inherently generates a piecewise harmonic incompatibility in the measured local field, whose Laplace is supported on the boundary of the region of interest (ROI). Based on such discovery, this project plans to propose a harmonic incompatibility removal based susceptibility reconstruction model by further analyzing the property of harmonic incompatibility in the measured local field data. This project also plans to develop an efficient numerical algorithm for the three-dimensional image restoration. Applications in real MR data will also be explored.

磁敏感定量成像(QSM)是一种通过磁共振信号中的相位数据求解场源反问题，从而使三维空间磁化率分布具象化的成像技术。但由于积分核的Fourier变换在频域上有零点，QSM涉及的反问题是不适定的。尽管众多的正则化计算模型克服了这一难点，导致实验结果不佳的场数据不相容这一问题却未引起足够的重视。我们在最近的研究工作中发现，在标准局域场中，即Laplace算子在感兴趣区域(ROI)成立的场中，QSM的数据采集过程会天然地产生分段谐波不相容性。基于这样的发现，本项目计划通过深入分析标准局域场数据谐波不相容性的性质，建立一类去除谐波不相容性的磁化率重构模型。除此目标外，我们的项目还将研究三维图像恢复的高效数值算法，而且实际MR数据中的应用也会是我们的探索目标之一。

在定量磁化率图标（QSM）中，背景场去除是一个重要的数据采集步骤，因为它通过在测量的局部场数据中产生谐波不兼容性而对恢复质量产生显著影响。尽管基于稀疏性的第一代谐波不兼容消除（1GHIRE）模型已经实现了优于传统方法的性能增益，但1GHIRE模型必须进一步改进，因为在背景消除的泊松方程的数值求解中存在基础失配。在本文中，我们提出了第二代谐波不兼容消除（2GHIRE）模型，以减少基失配，这是基于紧帧图像恢复中的平衡方法的启发。实验结果表明，所提出的2GHIRE模型在恢复质量和计算效率方面都具有优势。