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Local Inversions in Ultrasound Modulated Optical Tomography

Ultrasound modulated optical tomography, also called acousto-optics tomography, is a hybrid imaging modality that aims to combine the high contrast of optical waves with the high resolution of ultrasound. We follow the model of the influence of ultrasound modulation on the light intensity measurements developed in [Bal Schotland PRL 2010]. We present sufficient conditions ensuring that the absorption and diffusion coefficients modeling light propagation can locally be uniquely and stably reconstructed from the corresponding available information. We present an iterative procedure to solve such a problem based on the analysis of linear elliptic systems of redundant partial differential equations.