基于不等式约束的磁共振信号T2谱多指数分解法及算法改进

磁共振地下水探测信号的弛豫时间T₂和振幅与地下岩石孔隙大小和地下水的含水量直接相关。目前，磁共振地下水探测方法中，信号的衰减特性由平均弛豫时间T^*₂来描述。然而，对于复杂的多孔介质组成的岩石结构，仅由T^*₂无法准确描述地下孔隙情况。详细研究了基于不等式约束的多指数分解法，进行了信号T₂谱的提取，并重新计算多指数形式下的信号初始振幅。结果表明：对比信号在不同采集时间下的T₂谱提取结果，延长信号的采集时间有助于T₂谱的准确提取；通过磁共振仿真信号计算并分析不同信噪比下的T₂谱提取结果，信噪比大于30 dB时相对误差平均值小于5%；进行算法改进，得到信噪比大于10 dB时相对误差平均值小于5%的结果，且幅值和T₂的相对误差平均值降低了约1/3。由此可知:采用多指数分解法能够获得磁共振信号的T₂谱，正则化技术和加权修正能够提高T₂谱的准确度和抗干扰能力；与单指数方式相比，采用多指数拟合能够更准确地恢复信号初始振幅。

MRS Signal T2 Inversion by Multi-Exponential Decomposition with Inequality Constraint

The amplitude and relaxation time T₂ of magnetic resonance sounding (MRS) signal are directly related with water content and pore size of aquifers. Average T₂, denoted by T^*₂, is often used to describe the decay characteristic of MRS signal. However, in the case of porous media rock, pore size should be described by T₂ spectrum of MRS signal. To obtain the spectrum and estimate the initial amplitude more accurately, we studied multi-exponential decomposition method based on inequality constraint in this paper. Numerical results show that extending signal length helps the accuracy of T₂ spectrum estimation. With traditional method, average relative error is less than 5% when SNR is greater than 30 dB. With our modified algorithm, a SNR about 10 dB could lead to the same error. meanwhile, the error of the estimated amplitude is reduced by at least 1/3. It can be concluded that multi-exponential decomposition method could obtain T₂ spectrum of MRS signal, and adding regularization and weighted correction to the method could improve the accuracy of T₂ spectrum inversion. Comparing to mono-exponential fitting, multi-exponential inversion can estimate the initial amplitude more accurately.