Some lecture notes from recent courses on inverse problems.
- From a course taught at the University of Washington on "X-Ray Tomography and Transport Theory", Summer 2011:
- Guillaume Bal's lecture notes on generalized X-ray transforms: pdf.
- Francois Monard's lecture notes on the numerical aspects of X-ray transforms: pdf.
- Guillaume Bal's course notes on inverse problems: pdf.
- Cedric Bellis' lectures notes on transmission eigenvalues: pdf.
- Mikko Salo's lecture notes on Calderon's problem: pdf.
Some featured publications by the IP@AM members and collaborators.
- G. Bal, Hybrid inverse problems and internal information, submitted, 2011.
- G. Bal, Inverse Transport Theory and applications, Inverse Problems, 25, 055006, 2009.
Articles on inverse transport theory
- G. Bal and F. Monard, Inverse transport with isotropic time-harmonic sources, to appear in SIAM Journal of Mathematical Analysis, 2012.
- G. Bal, A. Jollivet, I. Langmore and F. Monard, Angular average of time-harmonic transport solutions, Communications in Partial Differential Equations, 1532-4133, Vol. 36, Issue 6, 2011, Pages 1044 - 1070.
- G. Bal and A. Jollivet, Time-dependent angularly averaged inverse transport, Inverse Problems, 25, 075010, 2009.
- G. Bal and A. Jollivet, Stability estimates for time dependent inverse transport, SIAM J. Math. Anal., 42(2), pp. 679-700, 2010
- G. Bal, I. Langmore and F. Monard, Inverse Transport with Isotropic Sources and Angularly Averaged Measurements, Inverse Probl. Imaging, 2(1), pp. 23-42, 2008
Articles on hybrid inverse problems
- F. Monard and G. Bal, Inverse anisotropic diffusion from power density measurements in two dimensions, submitted to Inverse Problems, 2011.
- F. Monard and G. Bal, Inverse diffusion problems with redundant internal information, submitted to Inverse Probl. Imaging, 2011.
- G. Bal, Cauchy problem for Ultrasound Modulated EIT, submitted, 2011.
- G. Bal, E. Bonnetier, F. Monard and F. Triki, Inverse diffusion from knowledge of power densities, submitted to Inverse Probl. Imaging, 2011.
- G. Bal and K. Ren, On Multi-spectral quantitative photoacoustic tomography, submitted.
- G. Bal and K. Ren, Multiple-source quantitative photoacoustic tomography, Inverse problems, 27(7), 075003, 2011.
- G. Bal and K. Ren, Non-uniqueness result for a hybrid inverse problem , to appear in Contemporary Mathematics, 2012.
- G. Bal, K. Ren, G. Uhlmann and T. Zhou, Quantitative Thermo-acoustics and related problems, Inverse Problems, 27(5), 055007, 2011.
- G. Bal and J.C. Schotland, Inverse Scattering and Acousto-Optic Imaging, Phys. Rev. Letters, 104, 043902, 2010
- G. Bal and G. Uhlmann, Inverse Diffusion Theory of Photoacoustics, Inverse Problems, 26(8), 085010, 2010
- G. Bal, A. Jollivet and V. Jugnon, Inverse Transport Theory of Photoacoustics, Inverse Problems, 26, 025011, 2010
Articles on Numerical Methods for transport
- F. Monard and G. Bal, An accurate solver for forward and inverse transport, J. Comp. Phys., 229, pp. 4952-4979, 2010
Articles on inverse scattering for the relativistic Newton equation
- A. Jollivet, On inverse problems in electromagnetic field in classical mechanics at fixed energy, J. Geom. Anal. 17:(2), 275--319 (2007).
- A. Jollivet, On inverse problems for the multidimensional relativistic Newton equation at fixed energy, Inverse Problems 23:(1), 231--242 (2007).
- A. Jollivet, On inverse scattering for the multidimensional relativistic Newton equation at high energies, J. Math. Phys. 47:(6) 062902, (2006).