基于稀疏度自适应压缩感知的电容层析成像图像重建算法

Image Reconstruction Algorithm for Electrical Capacitance Tomography Based on Sparsity Adaptive Compressed Sensing

为提高电容层析成像(ECT)系统重建图像的质量,该文提出一种基于改进稀疏度自适应的压缩感知电容层析成像算法。利用压缩感知与电容层析成像算法的契合点,以随机改造后的电容层析成像灵敏度矩阵为观测矩阵,离散余弦基为稀疏基,测量电容值为观测值,建立模型。利用线性反投影算法(LBP算法)所得图像预估原始图像稀疏度,以预估稀疏度值作为索引原子初始值进行稀疏度自适应迭代。改进后的稀疏度自适应匹配追踪重构算法实现ECT图像重建,解决了稀疏度预估不准确导致重建图像精度差的问题。仿真实验结果表明,该算法可以有效重建ECT图像,其成像质量优于LBP算法、Landweber算法、Tikhonov算法等传统算法,是研究电容层析成像图像重建的一种新的方法和手段。

In order to improve quality of the reconstructed images of the Electrical Capacitance Tomography （ECT） system, an improved sparsity adaptive matching pursuit compressed sensing algorithm is proposed. Based on the coherence point of Compressed Sensing （CS） theory and ECT, the CS-ECT model is established. In the model, the sensitivity matrix of ECT is designed in a random order to be the observation matrix, the discrete cosine base is used as the sparse base, the capacitance value is measured as the observed value. By using the Linear Back Projection （LBP） algorithm, the sparsity of the estimated images is confirmed. The sparsity can be served as the initial value of the atomic index for sparsity adaptive iteration. The lack of image reconstruction accuracy caused by the inaccurate estimate of sparsity can be solved by the improved sparsity adaptive matching pursuit algorithm. Simulation results indicate that reconstructed images with higher accuracy can be obtained using the improved sparsity adaptive matching pursuit compressed sensing algorithm than the LBP algorithm, Landweber algorithm and Tikhonov algorithm. A new method of ECT reconstruction is provided.