自适应阈值收缩算子的稀疏正则化图像重建算法

doi:10.7523/j.issn.2095-6134.2020.02.014

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

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

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

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/Abstract

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

中图分类号:

TP29

张胜男, 许燕斌, 董峰. 自适应阈值收缩算子的稀疏正则化图像重建算法[J]. 中国科学院大学学报, 2020, 37(2): 242-247.

ZHANG Shengnan, XU Yanbin, DONG Feng. Sparse regularization algorithm with adaptive shrinkage thresholding operator for image reconstruction[J]. , 2020, 37(2): 242-247.

参考文献

[1] Schroter T, Tautenhahn U. On the optimality of regularization methods for solving linear ill-posed problems[J]. Journal for Analysis and its Application, 1994, 13(4):697-710.
[2] Xu Y B, Pei Y, Dong F. An adaptive Tikhonov regularization parameter choice method for electrical resistance tomography[J]. Flow Measurement and Instrumentation, 2016, 50:1-12.
[3] 陈晓艳,房晓东. 一种新的正则化图像重建算法及参数优化[J]. 天津科技大学学报, 2014, 29(6):74-77.
[4] Natarajan B K. Sparse approximate solutions to linear systems[J]. Society for Industrial and Applied Mathematics, 1995, 24(2):227-234.
[5] Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J]. Communications on Pure and Applied Mathematics, 2004, 57(11):1413-1457.
[6] Bioucas-Dias J, Figueiredo M. A new TwIST:two-step iterative shrinkage/thresholding algorithms for image restoration[J]. IEEE Transactions on Image Processing, 2007, 16(12):2992-3004.
[7] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(1):183-202.
[8] Blumensath T, Davies M E. Iterative thresholding for sparse approximations[J]. Journal of Fourier Analysis and Applications, 2008, 14(5/6):629-654.
[9] Bredies K, Lorenz D A. Iterated hard shrinkage for minimization problems with sparsity constraints[J]. SIAM Journal on Scientific Computing, 2008, 30(2):657-683.
[10] Fornasier M, Rauhut H. Iterative thresholding algorithms[J]. Applied Computational Harmonic Analysis, 2008, 25(2):187-208.
[11] Voronin S, Woerdeman H J. A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints[J]. Applied Computational Harmonic Analysis, 2013, 35(1):151-164.
[12] Dickin F, Wang M. Electrical resistance tomography for process applications[J]. Measurement Science and Technology, 1996, 7(3):247-260.
[13] Gehre M, Kluth T, Lipponen A, et al. Sparsity reconstruction in electrical impedance tomography:an experimental evaluation[J]. Journal of Computational and Applied Mathematics, 2012, 236(1):2126-2136.
[14] 董峰, 赵佳, 许燕斌,等. 用于电阻层析成像的快速自适应硬阈值迭代算法[J]. 天津大学学报, 2015, 48(4):305-310.
[15] Ye J M, Wang H G, Yang W Q. Image reconstruction for electrical capacitance tomography based on sparse representation[J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(1):89-102.
[16] Zhao J, Xu Y B, Tan C, et al. A fast sparse reconstruction algorithm for electrical tomography[J]. Measurement Science and Technology, 2014, 25(8):085401.

自适应阈值收缩算子的稀疏正则化图像重建算法

Sparse regularization algorithm with adaptive shrinkage thresholding operator for image reconstruction

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