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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)

- Guillaume Bal
- 2009

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)

- Guillaume Bal
- 2012

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)

- Guillaume Bal, Ramón Verástegui
- Multiscale Modeling & Simulation
- 2004

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)

- Guillaume Bal
- 2006

This paper analyzes some properties of the parareal algorithm, which can be used to parallelize the time discretizations of differential equations. The parareal algorithm proceeds as follows. Firstly, a coarse time step is used to solve the equation sequentially on a given time interval. Secondly, a fine discretization is used to solve the evolution… (More)

- Guillaume Bal
- 2004

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)

We give a detailed mathematical analysis of the radiative transport limit for the average phase space density of solutions of the Schrödinger equation with time dependent random potential. Our derivation is based on the construction of an approximate martingale for the random Wigner distribution.

- Guillaume Bal, Kui Ren
- 2011

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)

Thermo-acoustic tomography is a hybrid medical imaging modality that aims to combine the good optical contrast observed in tissues with the good resolution properties of ultrasounds. Thermo-acoustic imaging may be decomposed into two steps. The first step aims at reconstructing an amount of electromagnetic radiation absorbed by tissues from boundary… (More)

- Guillaume Bal, Leonid Ryzhik
- SIAM Journal of Applied Mathematics
- 2000