B-Spline-Based Sharp Feature Preserving Shape Reconstruction Approach for Electrical Impedance Tomography

Liu, Dong; Gu, Danping; Smyl, Danny; Deng, Jiansong; Du, Jiangfeng

doi:10.1109/tmi.2019.2905245

Cited by 46 publications

(25 citation statements)

References 43 publications

(51 reference statements)

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“…The idea of accounting for shape information based regularization in the reconstruction is gaining increasing interest within the scientific community. Several recent studies [20]- [28] in both medical and industrial applications have explored applying prior shape information with the objective of improving image quality. Shape-based reconstruction methods have been employed with wide success to determine information concerning the size, shape, location and perhaps the number of anomalies across multiple application realms arising in medical imaging and industrial field.…”

Section: Introductionmentioning

confidence: 99%

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

Liu

2019

IEEE Trans. Med. Imaging

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This paper presents a new computational framework in electrical impedance tomography (EIT) for shape reconstruction based on the concept of moving morphable components (MMC).In the proposed framework, the shape reconstruction problem is solved in an explicit and geometrical way. Compared with the traditional pixel or shape-based solution framework, the proposed framework can incorporate more geometry and prior information into shape and topology optimization directly and therefore render the solution process more flexibility. It also has the afford potential to substantially reduce the computational burden associated with shape and topology optimization. The effectiveness of the proposed approach is tested with noisy synthetic data and experimental data, which demonstrates the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the proposed approach considering modeling errors caused by nonhomogeneous background, varying initial guesses, differing numbers of candidate shape components, and differing exponent in the shape and topology description function are performed. The simulation and experimental results show that the proposed approach is tolerant to modeling errors and is fairly robust to these parameter choices, offering significant improvements in image quality in comparison to the conventional absolute reconstructions using smoothness prior regularization and total variation regularization.

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Section: Introductionmentioning

confidence: 99%

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

Liu

2019

IEEE Trans. Med. Imaging

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“…tissue abnormalities. Some common modalities include X-ray tomography [2,3,4], electrical impedance tomography (EIT) [5,6,7,8,9,10], photoacoustic imaging/optical diffusion tomography [11,12,13], magnetic resonance imaging (MRI) [14,15], and elasticity imaging [16,17,18]. In the broad field of physical sciences, compiling a complete list of applications for inverse problems would be a dubious task.…”

Section: Introductionmentioning

confidence: 99%

Less is often more: Applied inverse problems using hp-forward models

Smyl

Liu

2019

Journal of Computational Physics

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“…The j th B ‐spline basis function B j,p ( t ) of degree p can be directly defined as shown in Equation (4). [ 34,35 ]

({, \begin{matrix} B_{j, 0} false(t false) = \{\begin{matrix} left 1 & left normalif t_{j} \leq t < t_{j + 1} \\ left 0 & left otherwise \end{matrix} \\ 0true B_{j, p} (t) = \frac{t - t_{j}}{t_{j + p} - t_{j}} B_{j, p - 1} (t) + \frac{t_{j + p + 1} - t}{t_{j + p + 1} - t_{j + 1}} B_{j + 1, p - 1} (t) \end{matrix})

…”

Section: Methodsmentioning

confidence: 99%

“…The jth B-spline basis function B j,p (t) of degree p can be directly defined as shown in Equation (4). [34,35]…”

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confidence: 99%

Numerically Denoising Thermally Tunable and Thickness‐Dependent Terahertz Signals in ErFeO₃ Based on Bézier Curves and B‐Splines

Zeng

Zhang

et al. 2021

Annalen der Physik

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The terahertz (THz) spectral range offers a platform for experimentally collecting electromagnetic pulses to analyze the intrinsic resonances of matter and has become an important field for applying intrinsic responses to future information devices. However, a lack of numerical methods for signal denoising exists in the knowledge of the THz spectral range. In this paper, numerical methods that employ the Bézier curve and its generalization (B‐spline) to denoise thermally tunable and thickness‐dependent terahertz signals are proposed. Different thicknesses of ErFeO3 are chosen and prepared. Both Bézier curves and B‐splines have the ability to denoise the signals and the effect of the Bézier curves on the noise is close to but slightly less than that of the B‐splines. Additionally, the B‐splines show a better noise reduction effect and have better signal strength stability and robustness than do the Bézier curves. Thus, B‐splines are applied to process the raw data, and quantitative insight into the trend of the resonant frequencies, peak heights, and transmittances of antiferromagnetic resonance and ferromagnetic resonance with temperature is obtained.

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B-Spline-Based Sharp Feature Preserving Shape Reconstruction Approach for Electrical Impedance Tomography

Abstract: This is a repository copy of B-spline based sharp feature preserving shape reconstruction approach for electrical impedance tomography.

Cited by 46 publications

References 43 publications

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

Less is often more: Applied inverse problems using hp-forward models

Numerically Denoising Thermally Tunable and Thickness‐Dependent Terahertz Signals in ErFeO₃ Based on Bézier Curves and B‐Splines

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B-Spline-Based Sharp Feature Preserving Shape Reconstruction Approach for Electrical Impedance Tomography

Abstract: This is a repository copy of B-spline based sharp feature preserving shape reconstruction approach for electrical impedance tomography.

Cited by 46 publications

References 43 publications

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography

Less is often more: Applied inverse problems using hp-forward models

Numerically Denoising Thermally Tunable and Thickness‐Dependent Terahertz Signals in ErFeO3 Based on Bézier Curves and B‐Splines

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Numerically Denoising Thermally Tunable and Thickness‐Dependent Terahertz Signals in ErFeO₃ Based on Bézier Curves and B‐Splines