基于压缩感知的电容层析成像图像重建算法

为提高电容层析成像（ECT）系统采样速率及重建图像质量，本文提出一种基于压缩感知理论的ECT图像重建算法.首先，应用离散Fourier变换基将原始图像灰度信号进行稀疏化处理；接着，从16电极ECT系统中随机选取14个电极按随机顺序进行激励，并按随机顺序测量不同电极之间电容值，得到测量电容信号并建立相应的观测矩阵；最后，采用L1范数正则化模型和原对偶内点法实现图像重建.仿真实验结果表明，基于压缩感知理论算法重建的图像其质量优于Landweber迭代算法，在节省采样时间的同时可实现较高精度的图像重建，为ECT图像重建的研究提供了一种新的手段.

Image Reconstruction Algorithm for Electrical Capacitance Tomography Based on Compressed Sensing

In order to improve the sampling rate and the quality of the reconstructed images of electrical capacitance tomography (ECT) system,a new ECT image reconstruction algorithm based on compressed sensing theory was proposed.Firstly,using the orthogonal basis of Discrete Fourier Transformation,the gray signals of original images can be transformed into sparse signals.Then,14 electrodes randomly selected from the 16 electrodes ECT system were excited randomly and the capacitance values between different electrode pairs were also measured in a random order.By this way,the capacitance signals and the corresponding observation matrix were obtained.Finally,using L1 regularization model and primal dual interior point method,the gray signals of original images were achieved.The simulation results showed that the quality of the reconstructed images were better than the corresponding images obtained by the Landweber iterative algorithm.Therefore,the algorithm proposed can reconstruct high precision images with less observation data,which provides a new method for ECT image reconstruction.