Bayesian Statistical Methods

Centre of Excellence in Computational Complex Systems Research

 

Neural Networks in Electrical Impedance Tomography

Researchers: Jouko Lampinen, Aki Vehtari, Tomas Martinsen, Jani Lahtinen,
Kimmo Leinonen (Ahlström Pumps), Jari Kaipio (University of Kuopio)

The project is part of the PROMISE project group.

In electrical impedance tomography (EIT) the aim is to recover the internal structure of an object based on impedance measurements from the surface. EIT is very promising technique for industrial tomoraphy (process monitoring) as the instruments are inexpensive, but the inverse problem for the image reconstruction is very difficult. We have developed a novel approach for the EIT inverse problem, where the problem is transformed to a more regular space (eigen space) and Bayesian neural network is used to approximate the inverse mapping. The method is highly competent with the state-of-the-art inverse methods, and provides many advantages over any other approach: the reconstruction is nearly five orders of magnitudes faster, facilitating real time reconstruction, and incorporating additional background knowledge or constraints is easy.

Figure 1a
Figure 1b

Example of reconstruction of gas bubble in liquid by Electrical Impedance Tomography (EIT). The left figure shows the potential field due to one current injection with opposite electrodes, based on FEM (Finite Element Method) solution. The right figure shows the reconstruction with Bayesian neural network. The color indicates the bubble probability and blue contour the detected bubble boundary.

The proposed approach is very fast. For example, reconstruction of the bubble in figure 1 requires about 2 ms of CPU time in a 600 Mhz alpha processor with the neural network approach and about 4 minutes with a state-of-the-art iterative inverse method using total variation regularization. In addition, the method has very high immunity to noise, making it promising technique for industrial applications of EIT.

References

  • Aki Vehtari and Jouko Lampinen (2000). Bayesian MLP neural networks for image analysis. Pattern Recognition Letters, 21(13-14):1183-1191. (Special Issue - Selected Papers from The 11th Scandinavian Conference on Image Analysis.) (PostScript) (PDF)

  • Jouko Lampinen, Aki Vehtari, and Kimmo Leinonen (1999). Application of Bayesian neural network in electrical impedance tomography. In IJCNN'99: Proceedings of the 1999 International Joint Conference on Neural Networks [CD-ROM], paper number 375. (PDF)

  • Jouko Lampinen, Aki Vehtari, and Kimmo Leinonen (1999). Using Bayesian neural network to solve the inverse problem in electrical impedance tomography. In B. K. Ersboll and P. Johansen, editors, SCIA'99: Proceedings of the 11th Scandinavian Conference on Image Analysis, volume 1, pages 87-93. The Pattern Recognition Society of Denmark. (PostScript)