Spatially-Adaptive Variational Reconstructions for Linear Inverse Electrical Impedance Tomography
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Spatially-Adaptive Variational Reconstructions for Linear Inverse Electrical Impedance Tomography M. Huska1 · D. Lazzaro1
· S. Morigi1
· A. Samorè1
· G. Scrivanti1
Received: 9 May 2020 / Revised: 5 August 2020 / Accepted: 11 August 2020 / Published online: 24 August 2020 © The Author(s) 2020
Abstract The inverse electrical impedance tomography (EIT) problem involves collecting electrical measurements on the smooth boundary of a region to determine the spatially varying electrical conductivity distribution within the bounded region. Effective applications of EIT technology emerged in different areas of engineering, technology, and applied sciences. However, the mathematical formulation of EIT is well known to suffer from a high degree of nonlinearity and severe ill-posedness. Therefore, regularization is required to produce reasonable electrical impedance images. Using difference imaging, we propose a spatially-variant variational method which couples sparsity regularization and smoothness regularization for improved EIT linear reconstructions. The EIT variational model can benefit from structural prior information in the form of an edge detection map coming either from an auxiliary image of the same object being reconstructed or automatically detected. We propose an efficient algorithm for minimizing the (non-convex) function based on the alternating direction method of multipliers. Experiments are presented which strongly indicate that using non-convex versus convex variational EIT models holds the potential for more accurate reconstructions. Keywords Ill-posed inverse problems · Variational approach · Electrical impedance tomography · Spatially-adaptive reconstruction
1 Introduction Electrical impedance tomography is an imaging technique that aims to reconstruct the inner conductivity distribution of a medium starting from a set of measured voltages registered by a series of electrodes that are positioned on the surface of the medium. EIT is therefore a nondestructive testing technique, meaning that it allows to analyse the property of a material or structure without causing damage. It can be considered a tomographic modality due to the fact that it generates images of the internal features of a body. However, if compared to other tomography techniques, EIT provides lower spatial resolution outputs, but data can be
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S. Morigi [email protected] Department of Mathematics, University of Bologna, Bologna, Italy
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Journal of Scientific Computing (2020) 84:46
acquired relatively fast (EIT temporal resolution is estimated in the order of millisecond) and the apparatus is more manageable. The first applications of EIT techniques date back to 1930 on geology [35], and to the mid 80s with the first clinical use by Brown and Barber. Since then EIT technology has had a huge development in various application fields. Applications of EIT in biomedical imaging range from clinical imaging for organ monitoring to cell monitoring in tissue engineering [27,28]. The promising advantages of thi
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