基于L_P范数的磁感应断层成像图像重建算法

An Image Reconstruction Algorithm Based on L_P-norm for Magnetic Induction Tomography

磁感应断层成像(MIT)图像重建是一个典型的病态问题,且其数值解不稳定。为了改善解的病态性而又能提高重建图像的质量,本文在变差正则化算法的基础上提出一种新的基于LP范数的变差正则化算法。该算法不仅有效地克服了MIT重建图像数值解的不稳定性,还提高了重建图像的质量,增强了重建图像的空间分辨能力。仿真实验结果表明,该算法所获得的重建图像质量好于Tikhonov正则化算法和变差正则化算法,为MIT提供了一种新的有效方法。

Magnetic induction tomography （MIT） image reconstruction is a typical ill-posed problem, and its numeri- cal solution is unstable. A new image reconstruction algorithm based on the Lp-norm, which solves the ill-posed in- verse problem of MIT and improves the quality of reconstructed image, is presented in this paper. The new algo- rithm not only overcomes the problem of numerical instability of the MIT image reconstruction, but also improves the quality of the reconstructed image and enhances the spatial resolution of the reconstructed image. Simulation re- suits showed that the quality of the reconstructed image obtained using the presented algorithm was better than that using Tikhonov regularization algorithm and that using the variation regularization algorithm, so it could be an effec- tive method for the MIT.