基于改进Landweber算法的ECT图像重建

ECT Image Reconstruction Based on Improved Landweber Algorithm

电容层析成像(Electrical Capacitance Tomography,ECT)系统图像重建算法中,Landweber算法在重建图像质量及实时性方面取得较好的折衷,然而该算法针对不同的流型存在迭代步数差别较大及半收敛等问题。针对上述问题,通过同伦摄动方法推导出二阶迭代公式;并针对二阶迭代公式谱半径可能影响算法收敛的问题,通过添加约束因子以获得一种全收敛的改进Landweber算法。实验结果表明,改进算法在相对误差及相关系数上均优于原Landweber算法及其他对比算法,从而验证了改进算法的收敛性及有效性。

For image reconstruction algorithm in the ECT(Electrical Capacitance Tomography)system,the Landweber algorithm obtains a good tradeoff between the reconstructed image quality and real-time performance.However,the algorithm is with difference in the iteration steps and semi-convergence for different flow patterns.In order to solve the above problems,this paper derives the second-order iterative formula by the homotopy perturbation method,and for the problem that the spectral radius of the second-order iterative formula may affect the convergence of the algorithm,an improved Landweber algorithm with full convergence is obtained by adding constraint factors.The experimental results show that the improved algorithm outperforms the original Landweber algorithm and other comparison algorithms in terms of relative error and correlation coefficient,and the results also verify the convergence and effectiveness of the improved algorithm.