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Sensitivity matrix construction based on ultrasound modulation for electrical resistance tomography

Image reconstruction of electrical resistance tomography (ERT) is an inherently nonlinear inverse problem. Sensitivity matrix is widely adopted to make this inverse problem to be a linear one. Usually, the sensitivity matrix employed is calculated under a uniform conductivity distribution. However, it is different from the sensitivity matrix of the measured object with inclusions, and the difference between them affects the quality of reconstructed image. Aiming at improving the resolution of reconstructed images, a novel way of constructing the sensitivity matrix is proposed based on ultrasound modulation. With focused ultrasound perturbing the measured object, the conductivity in each focal region will be altered according to the acousto-electric effect. Measuring the boundary voltage change with the corresponding change of the conductivity, then the sensitivity matrix of the measured object will be approximately constructed. The sensitivity matrices constructed based on the ultrasound modulation and on the Geselowitz's sensitivity theorem are presented and analyzed. With the proposed construction method, sensitivity matrix is more sensitive to the inclusion, even in the center of the measured object. Besides, image reconstruction is carried out by sensitivity algorithm using these two kinds of sensitivity matrix. Simulation results indicate that the reconstructed images with higher quality can be obtained with sensitivity matrix constructed based on the ultrasound modulation.