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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.

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)

We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a priori L 2-bounds available in the time-reversal… (More)

- 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)

- 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)

Transport theoretic boundary conditions are derived for acoustic wave reeection and transmission at a rough interface with small random uctuations. The Wigner distribution is used to go from waves to energy transport in the high frequency limit, and the Born expansion is used to calculate the eeect of the random rough surface. The smoothing method is also… (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
- SIAM Journal of Applied Mathematics
- 2002

This paper addresses the validity of radiative transfer equations as a model for the energy density of waves propagating in highly heterogeneous media. Comparisons between acoustic wave simulations over domains of size comparable to 500 wavelength in two space dimensions and Monte Carlo simulations of radiative transfer equations are performed. In the… (More)