Guillaume Bal

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This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photoacoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave(More)
Inverse transport consists of reconstructing the optical properties of a domain from measurements performed at the domain’s boundary. This paper concerns several types of measurements: time dependent, time independent, angularly resolved and angularly averaged measurements. We review recent results on the reconstruction of the optical parameters from such(More)
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multiwave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when they combine high contrast with high resolution. In some settings, a single modality displays either high contrast or high(More)
This paper analyzes the refocusing properties of time-reversed acoustic waves that propagate in different media during the forward and backward propagation phases. We show how the refocused signal is modified as the medium during backward propagation departs from the medium during forward propagation. The derivation is based on the analysis of the(More)
After stating an abstract convergence result for the parareal algorithm used in the parallelization in time of general partial differential equations, we analyze the stability and convergence properties of the algorithm for equations with constant coefficients. We show that suitably damping coarse schemes ensure unconditional stability of the parareal(More)
Photoacoustic tomography (PAT) is a novel hybrid medical imaging technique that aims to combine the large contrast of optical coefficients with the high resolution capabilities of ultrasound. We assume that the first step of PAT, namely the reconstruction of a map of absorbed radiation from ultrasound boundary measurement, has been done. We focus on(More)