3D electrical impedance tomography reconstructions from simulated electrode data using direct inversion \(\mathbf{t}^{\mathbf{exp}}\) and Calderón methods. (English) Zbl 1481.65211
Summary: The first numerical implementation of a \(\mathbf{t}^{\mathbf{exp}}\) method in 3D using simulated electrode data is presented. Results are compared to Calderón’s method as well as more common TV and smoothness regularization-based methods. The \(\mathbf{t}^{\mathbf{exp}}\) method for EIT is based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. In 2D, \(\mathbf{t}^{\mathbf{exp}}\) methods have shown great promise for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D \(\mathbf{t}^{\mathbf{exp}}\) and Calderón methods are demonstrated to provide comparable quality to their 2D counterparts and hold promise for real-time reconstructions due to their fast, non-optimized, computational cost.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 78A05 | Geometric optics |
| 92C55 | Biomedical imaging and signal processing |
Keywords:
\(\mathbf{t}^{\mathbf{exp}}\); Calderón; conductivity; complete electrode model; complex geometrical opticsReferences:
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