摘要
针对电容层析成像逆问题求解存在病态性和欠定性的问题,将压缩感知理论应用到成像过程中缓解其欠定性。首先将初始信号稀疏化处理,其次基于高斯随机阵对灵敏度矩阵的各行重新排列,随后进行奇异值分解得到了列独立性更高的观测矩阵。最后将基于l_(1/2)-范数的半阈值迭代算法引入到ECT成像过程中,并在罚函数中加入l_(2)-范数的约束项,通过改进的半阈值迭代算法进行求解。仿真实验表明,该算法有效地降低了图像误差,并兼顾了成像速度,在ECT成像过程中具有良好的性能。
To solve the problem of ill-posedness and underdetermination for the inverse problem of electrical capacitance tomography,the theory of compressed sensing was applied to the imaging process to alleviate its underdetermination.First,the initial signal was sparsed processing,and then the rows of the sensitivity matrix were rearranged based on the Gaussian random matrix,then the singular value decomposition(SVD)was used to obtain the observation matrix with higher column independence.Finally,the half-threshold iterative algorithm based on l_(1/2) norm was introduced into the ECT imaging process,and the constraint term of l_(2) norm was added to the penalty function,and solved by the improved semi-threshold iterative algorithm.The simulation experiment showed that the algorithm effectively reduced the image error and took into account the imaging speed,and had good performance in the ECT imaging process.
作者
马敏
刘一斐
刘亚楠
MA Min;LIU Yi-fei;LIU Ya-nan(College of Electronic Information and Automation,Civil Aviation University of China,Tianjin 300300,China)
出处
《计量学报》
CSCD
北大核心
2021年第5期595-602,共8页
Acta Metrologica Sinica
基金
国家自然科学基金委员会与中国民用航空局联合资助项目(U1733119)
民航科技项目(20150220)。
关键词
计量学
电容层析成像
半阈值迭代算法
图像重建
压缩感知
观测矩阵
metrology
electrical capacitance tomography
semi-threshold iterative algorithm
image reconstruction
compressed sensing
observation matrix
