Hughett P
Department of Electrical Engineering and Computer Sciences, Lawrence Berkeley Laboratory, University of California, Berkeley 94720, USA.
Ann Biomed Eng. 1995 Jul-Aug;23(4):506-23. doi: 10.1007/BF02584450.
Magnetic source imaging is the reconstruction of the current source distribution inside an inaccessible volume from magnetic field measurements made outside the volume. It is possible in many applications to estimate, from prior physiological and anatomical knowledge, the source positions, amplitudes, and correlations, as well as the noise amplitudes and correlations. The optimal constrained linear inverse method (OCLIM) uses this prior knowledge to obtain a minimum mean-square error estimate of the current distribution. OCLIM can be efficiently computed using the Cholesky decomposition, taking about a second on a workstation-class computer for a problem with 64 sources and 144 detectors. Any source and detector configuration is allowed as long as their positions are fixed a priori. Correlations among source and noise amplitudes are permitted. OCLIM reduces to the optimally weighted pseudoinverse method of Shim and Cho if the source amplitudes are independent and identically distributed and to the minimum-norm least-squares estimate in the limit of no measurement noise or no prior knowledge of the source amplitudes. In the general case, OCLIM has better mean-square error than either previous method. OCLIM appears well suited to magnetic imaging, since it exploits prior information, provides the minimum reconstruction error, and is inexpensive to compute.
磁源成像就是根据在体外进行的磁场测量来重建体内难以接近区域的电流源分布。在许多应用中，根据先前的生理和解剖学知识来估计源位置、幅度和相关性，以及噪声幅度和相关性是可行的。最优约束线性逆方法（OCLIM）利用这些先验知识来获得电流分布的最小均方误差估计。使用Cholesky分解可以高效地计算OCLIM，对于一个有64个源和144个探测器的问题，在工作站级计算机上大约需要一秒钟。只要源和探测器的位置事先固定，任何源和探测器配置都是允许的。允许源幅度和噪声幅度之间存在相关性。如果源幅度是独立同分布的，OCLIM就简化为Shim和Cho的最优加权伪逆方法；在没有测量噪声或没有源幅度的先验知识的极限情况下，OCLIM就简化为最小范数最小二乘估计。在一般情况下，OCLIM的均方误差比之前的任何一种方法都要好。OCLIM似乎非常适合磁成像，因为它利用了先验信息，提供了最小的重建误差，并且计算成本较低。
