摘要针对动态对比度增强磁共振灌注成像中脑血容积的计算，本文提出基于Hankel矩阵的奇异值分解（singular value decomposition，SVD）算法。在奇异值数目的确定上采用差分谱量级差的研究方法，对算法进行理论推导与仿真模拟，得到较为理想的滤波效果。由于成像过程存在测量噪声的干扰，分析了信噪比和示踪剂延迟对算法的影响。仿真结果表明，信噪比越低（SNR=5dB），算法处理效果越明显；信噪比增高（SNR=100dB），估计值偏差减小，结果越为准确。且该算法不受示踪剂延迟的影响。与传统奇异值分解算法相比，采用基于Hankel矩阵的奇异值算法可以更为准确地估计脑血容积。
Abstract：The singular value decomposition (SVD) method based on Hankel matrix is proposed in this paper to calculate cerebral blood volume (CBV) in dynamic contrast-enhanced perfusion magnetic resonance imaging. The method of differential spectral order error is proposed to determine the number of singular values. Through the theoretical derivation and simulation, the ideal filtering effect is reached. Because of the existing noise in the imaging process, the influences such as signal-to-noise ratio (SNR) and tracer delay are analyzed. The simulation results show that this method can more effectively estimate cerebral blood volume at the higher SNR(SNR=100dB) and is not affected by the tracer delay; while compared with the value of the cerebral blood volume before and after using the method, the superiority of the method is more obvious at the lower SNR (SNR=5dB). Compared with the traditional singular value decomposition, the SVD method based on Hankel matrix can estimate the cerebral blood volume accurately.
任雅姿,李颖,刘欢. 基于Hankel矩阵的奇异值分解法对脑血容积计算的研究[J]. 振动与冲击, 2016, 35(16): 38-42.
Ren Ya-zi Li Ying Liu Huan. Research on the Calculation of Cerebral Blood Volume Using SVD Method Based on Hankel Matrix. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(16): 38-42.
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