频域磁声耦合成像逆问题初步研究

Preliminary Study on Inverse Problem of Magneto-Acoustic Imaging in Frequency Domain

对频域磁声耦合成像方法逆问题进行初步研究,为实现基于频域处理方法的磁声电导率成像打下基础。应用复平面矢量方法,基于声源和频域幅值相位特性,研究频域磁声成像逆问题数学模型和重建方法。对频域磁声信号随声源空间位置和幅度变化特性进行仿真,对简单模型不同声源分布的频域逆问题进行仿真重建。建立多频率下的声源幅值和相位矢量方程组,利用非线性方程组的优化算法求解声源信息。利用铜丝仿体,对矢量求解方法和逆问题声源重建进行实验验证。频域幅值和相位满足复平面声源矢量叠加理论。利用矢量方法,初步实现两个声源样本的声源幅度和位置的重建,成像分辨率小于1 cm,实验的声源重建位置误差小于±0.4 mm。通过对频域磁声成像逆问题的重建研究,为后续进行复杂模型和真实组织的频域磁声重建研究打下基础,对实现高分辨率成像具有重要研究意义。

A preiliminary study on inverse problem of magneto-acoustic imaging was conducted in this paper to lay the foundation for magneto-acoustic imaging based on measuring method in frequency domain. Basing on the amplitude and phase characteristics of sonic source with different amplitude and distribution,the mathematical model and the reconstruction using vector method was investigated. Equations to vectors of different frequencies were set up. Optimization algorithm for nonlinear equations was used to solve the sound source location.Amplitude and phase characteristics with different source distributions and the reconstruction to the two sonic sources were simulated. The experiment on copper wire was performed to validate the vector theory and the reconstruction method. The summed amplitude and the phase were the vector summation of the points all over the sample. The sonic source distribution could be reconstructed,and the imaging resolution is less than 1 mm.The reconstructed error was less than ± 0. 4 mm. The reconstructed study on magneto-acoustic imaging method provided the fundamental to the study to complex tissue and the biomedical samples. It is significant to the magneto-acoustic imaging with a high resolution.