Open AccessA wavelet frame constrained total generalized variation model for imaging conductivity distribution
Author(s) -
Yanyan Shi,
Zhiwei Tian,
Meng Wang,
Xiaolong Kong,
Lei Li,
Feng Fu
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021074
Subject(s) - tikhonov regularization , regularization (linguistics) , electrical impedance tomography , inverse problem , total variation denoising , wavelet , algorithm , iterative reconstruction , computer science , mathematical optimization , augmented lagrangian method , mathematics , tomography , mathematical analysis , artificial intelligence , image (mathematics) , physics , optics
Electrical impedance tomography (EIT) is a sensing technique with which conductivity distribution can be reconstructed. It should be mentioned that the reconstruction is a highly ill-posed inverse problem. Currently, the regularization method has been an effective approach to deal with this problem. Especially, total variation regularization method is advantageous over Tikhonov method as the edge information can be well preserved. Nevertheless, the reconstructed image shows severe staircase effect. In this work, to enhance the quality of reconstruction, a novel hybrid regularization model which combines a total generalized variation method with a wavelet frame approach (TGV-WF) is proposed. An efficient mean doubly augmented Lagrangian algorithm has been developed to solve the TGV-WF model. To demonstrate the effectiveness of the proposed method, numerical simulation and experimental validation are conducted for imaging conductivity distribution. Furthermore, some comparisons are made with typical regularization methods. From the results, it can be found that the proposed method shows better performance in the reconstruction since the edge of the inclusion can be well preserved and the staircase effect is effectively relieved.