ECT图像重建中最小坡度正则化参数选择方法

电容层析成像图像重建反问题常常是不适定的.提出了一种在最小坡度曲线段中选择Tikhonov正则化参数的新方法用于求解这一不适定反问题.对于测量数据的干扰,不适定问题的一些正则化解比其他的解敏感程度低.该方法使用一定准则选取不敏感正则化解中的一个,将这个解对应的正则化参数作为最优值.通过仿真实验,针对两种典型介质分布,将基于最小坡度方法计算的正则化参数与流行的L-曲线法在电容测量数据施加噪声情况下的图像重建结果进行了比较.实验表明基于新方法的图像重建结果要好于L-曲线法.

The Minimum Slope Method for Choosing Regularization Parameter in ECT Image Reconstruction

Image reconstruction for electrical capacitance tomography is an inverse problem and is often ill posed.A new solution is proposed to the ill-posed inverse problem,i.e.,choosing the Tikhonov regularization parameter within the minimumslope curve segment.However,in the capacitance measurement data are perturbed, the sensitivities of some regularized solution to such ill-posed are lower than other solutions.For this reason,in the new solution a definitive criterion is taken to choose one of those insensitive regularized solution and a regularization parameter corresponding to the solution chosen is taken as the optimal value.Simulation tests of capacitance data measurement with noise were conducted and two typical permittivity distributions to compare the two results of image reconstruction to which the regularization parameter was calculated by choosing it within the minimum-slope curve segment and by the prevailing L-curve approach.It is shown that the effect of the image reconstruction by the former is better than by the latter.