Int. J. of Appl. Math. and Mech. Vol. 4 (2005), 20-34 INVERSION OF ELECTRICAL CAPACITANCE TOMOGRAPHY DATA BY SIMULATED ANNEALING: NON-LINEAR VERSUS LINEARIZED FORWARD MODELING R. Martin 1 , C. Ortiz-Aleman 1 , J. C. Gamio 1 , and S. Muñoz-Gonzalez 1 1 Instituto Mexicano del Petroleo, Mexico Email: jcortiz@imp.mx Received 31 January 2005; accepted 19 August 2005 ABSTRACT In this work we apply the simulated annealing (SA) inversion method to the reconstruction of permittivity images from electrical capacitance tomography (ECT) data. We test the SA inversion method using static physical models simulating some typical distribution patterns of two and three-component flows. The SA-based permittivity inversions have some advantages over other approaches based on linear least-squares inversion: they can find good solutions starting with poor initial models, can more easily implement complex a priori information, and do not introduce smoothing effects in the final permittivity distribution model. A major disadvantage comes from the fact that SA is computationally intensive and lead to relatively slow reconstructions. We establish comparisons between two variations of the SA inversion method: a first one where computation of the forward problem (i.e., to find the mutual capacitance data for a given permittivity distribution inside the sensor) is made in a non-linear fashion by using a finite-volume method (FVM); and a second one, where we employed a linearized numerically improved forward model based on the use of a sensitivity matrix. We found this last approach to be faster and more accurate than traditional linear methods. Finally, results of this work provided us some insight about the effects on permittivity estimation from ECT data caused by linearization of the forward model. Keywords: Capacitance tomography, simulated annealing, image reconstruction, finite volume method, sensitivity matrix. 1 INTRODUCTION Tomography methods are mainly employed for obtaining estimated images of a cross section of an object. X-ray tomography was the first to be developed (in 1960s) and its use is now routine not only in medicine but in some industrial applications as well (internal inspection of mechanical components and flaw detection in materials, for example). Since then a number of new tomography methods aimed at industrial processes have emerged, collectively known as process tomography (Williams and Beck 1995). The main goal of process tomography methods, which started to develop in the mid 1980s, is to produce an image of the phase or component distribution in an industrial process using only external sensors and without causing any perturbation to it (Figure 1).