电容层析成像系统图像重建稳定性研究

Study on the stability of image reconstruction of electrical capacitance tomographic systems

电容层析成像图像重建是一个不适定的反问题求解过程 ,敏感于测量投影的微小变化 ,难以重建稳定的管截面图像 .通过奇异值分解分析了成像系统产生不适定性的原因 ,采用阻尼最小二乘法改善了图像重建所对应的病态方程组的求解条件 ,有效克服了图像重建过程中的不适定性 。

The image reconstruction of electrical capacitance tomographic systems is an ill\|posed inverse problem and it is sensitive to the micro\|change of measurement projections. So it is difficult to reconstruct stable cross\|section images. By means of the decomposition of singular value, the ill\|posed reason of tomographic systems was analyzed. Damped least square method was used to improve the solution condition of the ill\|conditioned equation corresponding to image reconstruction so that the ill\|posed problem of image reconstruction is overcome. Stable cross\|sectional images are reconstructed.