A Fast Gauss-Newton Based ECT Algorithm with Automatic Adjustment of the Regularization Parameter

Gert Holler, Daniel Watzenig and Bernhard Brandstätter

Christian Doppler Laboratory for Automotive Measurement Technology, Institute of Electrical Measurement and Measurement Signal Processing, Graz University of Technology,

Kopernikusgasse 24/4, A-8010, Graz, Austria, holler@emt.tugraz.at

ABSTRACT

Electrical capacitance tomograms are usually computed by means of linear back projection (LBP) algorithms, due to their ease of implementation, and high computation speed. LBP, however, suffers from blurred images, which can be improved using a posterior iterative scheme like series model or Maxwell updates for the measured capacitances. In this paper we propose a method based on a Gauss-Newton scheme, which solves the nonlinear inverse problem directly incorporating an automatic calculation of the required regularization parameter. The correct choice of the regularization parameter is crucial for reconstruction, affecting both accuracy and computational cost. In this paper we compare a novel method to calculate the regularization parameter on the basis of condition numbers with the L-curve approach for noiseless data, as well as for data with Gaussian noise added.

Keywords Capacitance tomography, Jacobian matrix, L-curves, Regularization parameter