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Research on ECT Image Reconstruction Algorithm Based on lp-norm |
MA Min,SUN Mei-juan,LI Ming |
College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China |
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Abstract In the process of ECT image reconstruction, non-convex compressed sensing algorithm based on lp-norm often has the problem of large computational complexity, and the algorithms corresponding to the proximal mapping of the regularization lp-norm minimization are limited to few specific values of parameter p, which leads to low image resolution. The improved interpolation function is used to replace xpp, by adjusting the parameters, the improved function is infinitely approximated to xpp. At the same time, the threshold representation theory is introduced, and based on it. A new adaptive threshold iterative algorithm is proposed to solve the new model. The experimental results show that the improved algorithm has stronger adaptability, higher image resolution and faster imaging speed than the Lanweber algorithm and iterative reweighted least squares method.
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Received: 08 April 2019
Published: 28 August 2020
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Fund:The National Natural Science Foundation of China |
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[1]张立峰, 李佳, 田沛. Kalman滤波在电容层析成像图像重建中的应用[J]. 计量学报, 2017, 38(3): 315-318.
Zhang L F, Li J, Tian Pei. Kalman Filtering in Electrical Capacitance Tomography Image application in reconstruction[J]. Acta Metrologica Sinica, 2017, 38(3): 315-318.
[2]马敏, 王伯波, 闰超奇, 等. 基于旋转电极的电容层析成像技术图像融合算法[J]. 计量学报, 2018, 39(1): 43-46.
Ma M, Wang B B, Yan C Q, et al. Image Fusion Algorithm-Based Rotating Electrodes for Electrical Capa-citance Tomography[J]. Acta Metrologica Sinica, 2018, 39(1): 43-46
[3]Candes E J. Robust uncertainty principles and signal recovery[C]//The 2nd Int Conf Computational Harmonic Anaysis. Nashville, TN, 2004.
[4]马坚伟, 徐杰, 鲍跃全, 等. 压缩感知及其应用: 从稀疏约束到低秩约束优化[J]. 信号处理, 2012, 28(5): 609-623.
Ma J W, Xu J, Bao Y Q, et al. Compressed sensing and its application: from sparse constraints to low rank constr-ained optimization[J]. Signal Processing, 2012, 28(5): 609-623
[5]张淑清, 胡永涛, 王世豪, 等. 基于混合采样的压缩感知重构算法[J]. 计量学报, 2017, 38(1): 69-72.
Zhang S Q, Hu Y T, Wang S H, et al. Co mpressed Sensing Reconstruction Algorithm Based on Hybrid Samp-ling[J]. Acta Metrologica Sinica, 2017, 38(1): 69-72.
[6]戴琼海, 付长军, 季向阳. 压缩感知研究[J]. 计算机学报, 2011, 34(3): 3425-3434.
Dai Q H, Fu C J, Ji X Y. Research on Compressed Sensing[J]. Chinese Journal of Computers, 2011, 34(3): 3425-3434.
[7]Baraniuk R G. Compressive Sensing[Lecture Notes][J]. IEEE Trans on Signal Processing Magazine, 2007, 24(4): 118-121.
[8]Candes E J, Donoho D L. Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Ed-ges[R]. 1999, Technical report, Department of Statistics, Stanford University.
[9]蒋沉, 苗生伟, 罗华柱, 等. 1p范数压缩感知图像重建优化算法[J]. 中国图象图形学报, 2017, 22(4): 435-442.
Jiang S, Miao S W, Luo H Z, et al. 1p-norm compressed sensing image reconstruction optimization algorithm[J]. Journal of Image and Graphics, 2017, 22(4): 435-442.
[10]Donoho D L. Compressed sensing[J]. IEEE Transac-tions on Information Theory, 2006, 52(4): 1289-1306.
[11]Szarek S J. Condition numbers of random matrices[J]. Journal of Complexity, 1991, 7(2): 131-149.
[12]Peng Jigen, Yue Shigang, Li Haiyang. NP/CMP Equivalence: A phenomenon hidden among sparsity Models l0 minimization and lp minimization for informa-tion processing[J]. IEEE Transactionon Information Theory, 2015, 61(7): 4028-4033.
[13]Cao Wenfei, Sun Jian, Xu Zongben. Fast image deconvolution using closed form thresholding formulas of regularization[J]. Journal of Visual Communication and Image Representation, 2013, 24(1): 31-41.
[14]Daubechies I, Defrise M, Mol C D. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J]. Communications on pure and applied mathematics, 2004, 57(11): 1413-1457. |
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