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Non-linear optimization methods for acousto-electric tomography

Dr. Souvik Roy
Dr. Souvik Roy
When May 01, 2018
from 04:00 PM to 05:00 PM
Where LH 006
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Abstract: Acousto-electric tomography (AET) is an hybrid imaging modality which combines the classical electrical impedance tomography (EIT) with ultrasound imaging. In this imaging technique, the object is probed with direct or alternating electric currents and voltages at the boundary of the body and focused ultrasound waves in the exterior. This leads to a perturbation of the interior conductivity and the response in the electrostatic boundary field is measured. In turn, this allows for the computation of the local electric energy density (power density) in the interior of the object. The inverse problem is to reconstruct the conductivity from several power density measurements. The reconstructions in AET are supposed to combine the high contrast advantage of EIT and high resolution advantage of ultrasound imaging.

The existing computational frameworks for solving this inverse problem relies primarily on linearisation techniques. Very less has been explored in a complete non-linear setup. Moreover, the existing algorithms do not demonstrate high contrast in the reconstructions. The aim of this research is to offer a new optimization approach for AET reconstruction in order to achieve a satisfactory balance between high resolution and high contrast images. A wide class of regularizations, including sparsity, coupled with Perona-Malik edge enhancing technique are used. Several numerical experiments performed using non-linear conjugate gradient and non-smooth proximal schemes demonstrate the effectiveness of our framework for high contrast and high resolution reconstruction of objects with occlusions and inclusions.

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