A fast Tikhonov regularization method based on homotopic mapping for electrical resistance tomography

Li, Shouxiao; Wang, Huaxiang; Liu, Tonghai; Cui, Ziqiang; Chen, Joanna N.; Xia, Zihan; Guo, Qianqian

doi:10.1063/5.0077483

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…In [127], the prior regularization filter was modified to incorporate a priori knowledge of lung structure for lung cancer monitoring. Furthermore, in [128], homotopic mapping was adopted in an iterative Tikhonov regularization scheme, along with a Krylov subspace-based projection to improve both spatial and temporal resolution. Finally, in [129], a direct Landweber approach is used for two-phase flow electrical resistivity imaging in a phantom with acrylic rods.…”

Section: Tikhonov and L 2 -Norm Regularizationmentioning

confidence: 99%

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

Dimas,

Alimisis,

Uzunoglu

et al. 2024

IEEE Access

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Electrical Impedance Tomography (EIT) has emerged as a valuable medical imaging modality, which visualizes the conductivity distribution of a subject by performing multi-electrode impedance measurements. EIT finds applications in monitoring lung and cardiac function, brain imaging and the detection of malignant tissues. Its mobility, outstanding temporal resolution and the absence of ionizing radiation make it particularly suitable for repetitive real-time monitoring and diagnostics, especially in radiation-sensitive populations, such as neonates. This paper presents a methodological review of EIT image reconstruction approaches spanning from traditional linear regularization and back-projection to more recent techniques, including deep learning, sparse Bayesian learning and non-linear shape-driven reconstruction. Linear and non-linear reconstruction approaches are distinguished, as well as time, frequency difference and absolute reconstruction ones. The exposition includes a concise elaboration of the methodologies' mathematical foundations and algorithmic deployment, with particular attention to recent advancements. For each approach, an assessment of its merits and drawbacks is given, providing implementation considerations, imaging performance and relevant applications.

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Section: Tikhonov and L 2 -Norm Regularizationmentioning

confidence: 99%

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

Dimas,

Alimisis,

Uzunoglu

et al. 2024

IEEE Access

View full text Add to dashboard Cite

show abstract

“…Meanwhile, the noise in measurement also causes randomness of the data. Previous researches have indicated that regularization is an effective way to alleviate these problems [13][14][15][16][17]. By incorporating the measurement data and a priori information, a reasonable solution consistent with both the data and the a priori knowledge can be obtained.…”

Section: Introductionmentioning

confidence: 99%

On the Image Reconstruction of Capacitively Coupled Electrical Resistance Tomography (CCERT) with Entropy Priors

Soleimani

Jiang

et al. 2023

Entropy

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Regularization with priors is an effective approach to solve the ill-posed inverse problem of electrical tomography. Entropy priors have been proven to be promising in radiation tomography but have received less attention in the literature of electrical tomography. This work aims to investigate the image reconstruction of capacitively coupled electrical resistance tomography (CCERT) with entropy priors. Four types of entropy priors are introduced, including the image entropy, the projection entropy, the image-projection joint entropy, and the cross-entropy between the measurement projection and the forward projection. Correspondingly, objective functions with the four entropy priors are developed, where the first three are implemented under the maximum entropy strategy and the last one is implemented under the minimum cross-entropy strategy. Linear back-projection is adopted to obtain the initial image. The steepest descent method is utilized to optimize the objective function and obtain the final image. Experimental results show that the four entropy priors are effective in regularization of the ill-posed inverse problem of CCERT to obtain a reasonable solution. Compared with the initial image obtained by linear back projection, all the four entropy priors make sense in improving the image quality. Results also indicate that cross-entropy has the best performance among the four entropy priors in the image reconstruction of CCERT.

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On adaptive block coordinate descent methods for ridge regression

Wei,

Shi,

Nie

et al. 2023

Comp. Appl. Math.

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A fast Tikhonov regularization method based on homotopic mapping for electrical resistance tomography

Cited by 4 publications

References 33 publications

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

On the Image Reconstruction of Capacitively Coupled Electrical Resistance Tomography (CCERT) with Entropy Priors

On adaptive block coordinate descent methods for ridge regression

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