Institute of Medical Engineering, University of Lübeck, Lübeck, Germany.
Phys Med Biol. 2010 Mar 21;55(6):1577-89. doi: 10.1088/0031-9155/55/6/003. Epub 2010 Feb 17.
Magnetic particle imaging (MPI) is a new imaging technique capable of imaging the distribution of superparamagnetic particles at high spatial and temporal resolution. For the reconstruction of the particle distribution, a system of linear equations has to be solved. The mathematical solution to this linear system can be obtained using a least-squares approach. In this paper, it is shown that the quality of the least-squares solution can be improved by incorporating a weighting matrix using the reciprocal of the matrix-row energy as weights. A further benefit of this weighting is that iterative algorithms, such as the conjugate gradient method, converge rapidly yielding the same image quality as obtained by singular value decomposition in only a few iterations. Thus, the weighting strategy in combination with the conjugate gradient method improves the image quality and substantially shortens the reconstruction time. The performance of weighting strategy and reconstruction algorithms is assessed with experimental data of a 2D MPI scanner.
磁性粒子成像（MPI）是一种新的成像技术，能够以高时空分辨率对超顺磁粒子的分布进行成像。为了重建粒子分布，必须求解一个线性方程组。这个线性系统的数学解可以使用最小二乘法来获得。在本文中，我们表明通过使用矩阵行能量的倒数作为权重来引入加权矩阵，可以提高最小二乘解的质量。这种加权的另一个好处是，迭代算法（如共轭梯度法）可以快速收敛，仅需几次迭代就能得到与奇异值分解相同的图像质量。因此，加权策略与共轭梯度法相结合，可以提高图像质量，并大大缩短重建时间。通过二维 MPI 扫描仪的实验数据评估了加权策略和重建算法的性能。
