基于改进极小范数解的电容层析成像图像重建算法

An Image Reconstruction Algorithm Based on the Improved Minimum Norm Solution for Electrical Capacitance Tomography

提出了一种新的电容层析成像图像重建算法。在分析极小范数解的基础上,针对电容层析成像(ECT)逆问题的特点,利用正则技巧对其进行改进,并利用奇异值分解定理分析了这种改进的数值稳定作用。在此基础上,利用加权技巧建立新的目标泛函进一步改进极小范数解,并在求解该泛函的过程中采用正则技巧确保数值解的稳定性。数值实验表明,该算法是有效的,能够有效地克服ECT图像重建的数值不稳定性;而且该算法计算直接、无需任何复杂的技巧;就该文所考察的重建对象而言,其图像重建质量好于线性反投影算法(LBP)、标准Tikhonov正则法和投影Landweber迭代法。从而为ECT图像重建提供了一种新的有效方法。

A novel image reconstruction algorithm for electrical capacitance tomography （ECT） was presented. According to the characteristic of the inverse problems of ECT, the minimum norm solution was improved using regularization technique, and the stability of the numerical solution was analyzed via singular value decomposition principle. A new objective function was established using weight technique, which improved minimum norm further. In the process of solving the function, regularization technique was employed to ensure the stability of numerical solution. Numerical experiments indicate the algorithm is efficient, and it can overcome efficiently numerical instability of the image reconstruction of ECT; furthermore, the computation of the algorithm is direct, and has not any complex technique; in the case of the considered reconstruction objects, the quality of the reconstructed image using the improved algorithm is better than the compared image reconstruction algorithms such as LBP, standard Tikhonov regularization and projective Landweber iteration algorithm. As a result, a new and efficient method is introduced to the image reconstruction of ECT.