基于改进FOCUSS算法的电容层析成像算法研究

针对电容层析成像(electrical capacitance tomography，ECT)逆问题求解的病态性和不适定性，在压缩感知(compressed sensing，CS)的基础上，提出一种改进FOCUSS的ECT重建算法。采用离散余弦变换(DCT)基将原始图像灰度信号进行稀疏化处理，在使用正则化FOCUSS算法求解的过程中引入拟牛顿法逼近求解中间稀疏变量，以提高信号重构的准确性。仿真实验结果表明，同LBP、Tikhonov和Landweber和FOCUSS算法相比，改进的FOCUSS算法能够有效区分物场中的不同介质，改善图像过度平滑的问题，减小图像误差至0.23，提高图像相关系数至0.80，具有更好的成像效果，为ECT图像重建算法的研究提供新的思路。

Image reconstruction algorithm for electrical capacitance tomography based on improved FOCUSS algorithm

On the basis of compressed sensing(CS) , this paper proposed an improved FOCUSS algorithm for the reconstruction of electrical capacitance tomography (ECT) , which aiming at the ill-conditionedness and ill-posedness of the inverse problem of ECT. The discrete cosine transform (DCT) basis made the grayscale signals of original images sparse. In the process of solving the inverse problem by employing the regularized FOCUSS algorithm, it introduced the quasi-Newton method to approximate and solve the intermediate sparse variables to improve the accuracy of signal reconstruction. Results of the simulation show that compared with LBP, Tikhonov, Landweber and FOCUSS algorithm, the improved FOCUSS algorithm can effectively distinguish the different media in the substance field, alleviate the over-smoothing effect, reduce the image error between the original image and the reconstructed image to 0.23, increase the correlation coefficient to 0.80, offer better image quality, and provide a new idea for the research on the algorithm for the reconstruction of ECT.