基于改进半阈值迭代算法的ECT图像重建

doi:10.3969/j.issn.1000-1158.2021.05.09

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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。

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	马敏
	刘一斐
	刘亚楠

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

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.

Key words： metrology electrical capacitance tomography semi-threshold iterative algorithm image reconstruction compressed sensing observation matrix

收稿日期: 2019-09-09 发布日期: 2021-05-24

PACS:

TB937

基金资助: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)

作者简介: 马敏(1971-),女,安徽霍邱人,中国民航大学教授,主要从事无损检测技术及新型传感器方面的研究。Email: mm5739@163.com

引用本文:

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.
MA Min,LIU Yi-fei,LIU Ya-nan. ECT Image Reconstruction Based on Improved Half-threshold Iterative Algorithm. Acta Metrologica Sinica, 2021, 42(5): 595-602.

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http://jlxb.china-csm.org:81/Jwk_jlxb/CN/10.3969/j.issn.1000-1158.2021.05.09 或 http://jlxb.china-csm.org:81/Jwk_jlxb/CN/Y2021/V42/I5/595

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