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中国科学院大学学报 ›› 2020, Vol. 37 ›› Issue (2): 242-247.DOI: 10.7523/j.issn.2095-6134.2020.02.014

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自适应阈值收缩算子的稀疏正则化图像重建算法

张胜男, 许燕斌, 董峰   

  1. 天津大学电气自动化与信息工程学院 天津市过程检测与控制重点实验室, 天津 300072
  • 收稿日期:2019-03-12 修回日期:2019-05-08 发布日期:2020-03-15
  • 通讯作者: 许燕斌
  • 基金资助:
    国家自然科学基金(61671322,61571321)和天津市自然科学基金(16JCYBJC18600)资助

Sparse regularization algorithm with adaptive shrinkage thresholding operator for image reconstruction

ZHANG Shengnan, XU Yanbin, DONG Feng   

  1. Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
  • Received:2019-03-12 Revised:2019-05-08 Published:2020-03-15

摘要: 针对图像重建中采用稀疏正则化算法时,阈值收缩算子的阈值参数难以选取的问题,提出一种采用自适应阈值收缩算子的稀疏正则化算法。该算法收缩算子的阈值参数在迭代求解过程中根据解的稀疏度进行更新;同时在该算子中引入权重系数,研究阈值算子的衰减特性对图像重建质量的影响;并将该算法应用于电学层析成像的仿真和实验图像重建。结果表明:与传统的稀疏正则化算法相比,使用具有衰减特性的阈值收缩算子的稀疏正则化算法重建图像的性能指标有所提高。当被测物场的内含物分布较为简单时,采用较大的权重系数;当被测物场的内含物分布相对复杂时,使用较小的权重系数,有利于提高重建图像的质量。

关键词: 图像重建, 稀疏正则化算法, 阈值收缩算子, 自适应, 衰减特性

Abstract: A sparse regularization algorithm with an adaptive shrinkage thresholding operator is proposed. In the operator the thresholding parameter can be updated according to the sparsity of the solution during iteration process, since the thresholding parameter is hard to select in sparse regularization algorithm for image reconstruction. In addition, a weight coefficient is introduced in the thresholding operator, and the effect of attenuation characteristics on image reconstruction quality is studied. The feasibility of this proposed algorithm is validated by image reconstruction of electrical tomography. The results show that the performance of images reconstructed using the sparse regularization algorithm with the proposed adaptive shrinkage thresholding operator is better than that using traditional shrinkage thresholding algorithm. When the distribution of the measured field is relatively simple, a larger weight coefficient is adopted. When the distribution of the measured field is relatively complicated, a smaller weight coefficient is used, which is beneficial to improve the quality of the reconstructed image.

Key words: image reconstruction, sparse regularization algorithm, shrinkage thresholding operator, adaptive, attenuation characteristics

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