Bayesian experimental design for head imaging by electrical impedance tomography. (English) Zbl 07906767
Summary: This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 62K05 | Optimal statistical designs |
| 62F15 | Bayesian inference |
| 65F10 | Iterative numerical methods for linear systems |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 78A30 | Electro- and magnetostatics |
| 78A70 | Biological applications of optics and electromagnetic theory |
| 92C55 | Biomedical imaging and signal processing |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35R25 | Ill-posed problems for PDEs |
| 35R30 | Inverse problems for PDEs |
Keywords:
electrical impedance tomography; head imaging; Bayesian experimental design; A-optimality; adaptivity; edge-promoting prior; lagged diffusivityReferences:
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