In this contribution we present a method for solving the inverse problem in electric impedance tomography with neural networks. The problem of reconstructing the conductivity distribution inside an object from potential measurements on the surface is known to be ill-posed requiring efficient regularization techniques. We demonstrate that a statistical inverse solution, where the mean of the inverse mapping is approximated with a neural network gives promising results. We study the effect of input and output data representation by simulations and conclude that projection to principal axis is feasible data transformation. Also we demonstrate that Bayesian neural networks, which aim to average over all network models weighted by the model's posterior probability provide the best reconstruction results. With the presented approach estimation of some target variables, such as the void fraction (the ratio of gas and liquid), may be applicable directly without the actual image reconstruction. We also demonstrate that the solutions are very robust against noise in inputs.
[1]
Heekuck Oh,et al.
Neural Networks for Pattern Recognition
,
1993,
Adv. Comput..
[2]
Radford M. Neal.
Assessing Relevance determination methods using DELVE
,
1998
.
[3]
A. Y. Nooralahiyan,et al.
Three-component tomographic flow imaging using artificial neural network reconstruction
,
1997
.
[4]
Andy Adler,et al.
A neural network image reconstruction technique for electrical impedance tomography
,
1994,
IEEE Trans. Medical Imaging.
[5]
Richard A Williams,et al.
Use of PCA and neural netwroks to extract information from tomographic images for process control
,
1997
.
[6]
Jouko Lampinen,et al.
Bayesian Neural Network to Solve the Inverse Problem in Electrical Impedance Tomography
,
1999
.
[7]
Geoffrey E. Hinton,et al.
Bayesian Learning for Neural Networks
,
1995
.
[8]
Jari P. Kaipio,et al.
Electrical impedance tomography with basis constraints
,
1997
.