Estimating shapes and free surfaces with electrical impedance tomography

Electrical impedance tomography (EIT) is a diffuse imaging modality in which the resistivity distribution inside the object is estimated based on electrical measurements made on the boundary. Several applications can be found in geophysics, medicine and industry. Image reconstruction is an iterative procedure in which the norm between the computed and measured voltages is minimized. Also, an additional regularization term is included in the minimized functional due to the ill-posedness of the problem. In the reconstruction process, the geometry of the object is assumed to be known. Geometry is known in many cases but there are various situations in which the shape of the domain is unknown. For example, in medical applications the shape of the domain, a part of the human body on which the measurement electrodes are attached, is unknown unless some other imaging modality is used for receiving the shape. In industrial applications, such as in the imaging of a stirrer vessel for detecting air distribution or detecting large air bubbles in pipelines, the free surface between the liquid and air is unknown and should be estimated. Within the domain we may also have 'voids' having zero conductivity and we might be interested in detecting the shapes and locations of the voids. An example could be the detection of corrosion faults in metallic plates. In this paper, two approaches for shape and free surface estimation are proposed. The approaches taken here are based on the idea used in shape optimization problems. In the first approach, the unknown shape is parametrized using the mesh nodes as parameters. In the second approach, we define new 'design variables' which are used as parameters. These design variables are the coefficients of a Bezier curve that defines the shape of the surface. In this paper, we show results of the free surface estimation from both computer simulations and tank measurements. Also, results of simultaneous reconstruction of the resistivity distribution and the free surface are shown. Comparison of the results between these two approaches will be given. The comparison shows better performance in the Bezier curve approach.

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