低复杂度的 fMRI 脑激活区定位的盲分离算法

摘 要：功能磁共振成像(FMRI)是一种医学影像技术，由于具有非侵入性和较高的时空分 辨率等优点现已被广泛应用于脑区定位。然而传统的 FMRI 信号分离算法复杂度太高，运行时 间长，不利于 FMRI 技术更有效地应用于脑功能的研究。针对传统 FMRI 脑区分离算法的计算 复杂度问题，提出了一种基于二阶哈达码变换的盲分离算法。先计算 fMRI 数据中血氧水平依 赖(BOLD)信号的相关函数，然后对其进行特征值分解得到解混矩阵，以此实现激活脑区定位。 由于哈达码只由 1 或?1 构成，因此可减少 BOLD 信号相关矩阵计算的复杂度。仿真结果表明， 相比高阶统计量的独立分量分析(ICA)和二阶统计量的傅里叶变换盲分离算法，该算法的计算时 间分别只有其 25%和 50%，而定位误差却较为接近。

A blind separation algorithm with low complexity for fMRI brain activation

Abstract: Functional magnetic resonance imaging (FMRI) is a medical imaging technology widely employed in brain region positioning for its non-invasiveness and high spatiotemporal resolution. However, the traditional FMRI signal separation algorithm was too complex and time-consuming to effectively apply the FMRI technology to brain function research. Aiming at the computational complexity of traditional FMRI brain separation algorithms, a blind separation algorithm was proposed based on the second-order Hadamard transform. This algorithm first calculated the correlation function of the blood oxygen level dependent (BOLD) signal in the fMRI data, and then performed eigenvalue decomposition to obtain the unmixing matrix, thereby realizing the activation of brain regions. Given the composition of the Hadamard being only 1 or ?1, the complexity can be reduced for the BOLD signal correlation matrix calculation. The simulation results show that compared with the independent component analysis (ICA) of high-order statistics and the Fourier transform blind separation algorithm of second-order statistics, the calculation time of this algorithm was only 25% and 50% of theirs, respectively, while the positioning error was close.