改进的Tikhonov正则化图像重建算法

Improved Tikhonov Regularization Method for Image Reconstruction

Tikhonov正则化法可以解决电容层析成像中图像重建的病态问题,同时能够平衡解的稳定性与精确性,但其有效性和成像质量受到测量数据粗差的影响。改进的Tikhonov正则化法将2范数和M-估计结合,用一个缓慢增长的Cauchy函数代替最小二乘法的平方和函数,提高了估计稳健性和适应性。利用COMSOL和MATLAB软件对方法的有效性进行验证,重建结果表明,改进的Tikhonov正则化法能够有效减少粗差影响,提高重建图像精确度及分辨率。

Tikhonov regularization method can resolve the ill-posedness of the inverse problem and balance the stability and accuracy of the solution in electrical capacitance tomography image reconstruction. However, its effectiveness can be seriously affected by the gross error of measurement data. Improved Tikhonov regularization method combines 2-norm and robust estimation, substitute a slower-growing Cauchy function for the quadratic sum in the least square method to further improve the robustness and adaptability of least square estimation. The effectiveness of the developed method is verified by COMSOL and MATLAB software. Reconstruction results demonstrate that the improved Tikhonov regularization method can effectively reduce influence of the gross error and improve image reconstruction accuracy and spatial resolution.