基于改进半阈值迭代算法的ECT图像重建

马敏; 刘一斐; 刘亚楠

doi:10.3969/j.issn.1000-1158.2021.05.09

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计量学报 ›› 2021, Vol. 42 ›› Issue (5) : 595-602. DOI: 10.3969/j.issn.1000-1158.2021.05.09

流量计量

基于改进半阈值迭代算法的ECT图像重建

马敏,刘一斐,刘亚楠

作者信息 +

ECT Image Reconstruction Based on Improved Half-threshold Iterative Algorithm

MA Min,LIU Yi-fei,LIU Ya-nan

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文章历史 +

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l1/2-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l2-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。

Abstract

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 l1/2 norm was introduced into the ECT imaging process, and the constraint term of l2 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.

导出引用

马敏,刘一斐,刘亚楠. 基于改进半阈值迭代算法的ECT图像重建[J]. 计量学报. 2021, 42(5): 595-602 https://doi.org/10.3969/j.issn.1000-1158.2021.05.09

MA Min,LIU Yi-fei,LIU Ya-nan. ECT Image Reconstruction Based on Improved Half-threshold Iterative Algorithm[J]. Acta Metrologica Sinica. 2021, 42(5): 595-602 https://doi.org/10.3969/j.issn.1000-1158.2021.05.09

中图分类号： TB937

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