IP@AM

Course Material

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.

Publications

Some featured publications by the IP@AM members and collaborators.

Topical reviews

1. G. Bal, Hybrid inverse problems and internal information, submitted, 2011.
2. G. Bal, Inverse Transport Theory and applications, Inverse Problems, 25, 055006, 2009.

Articles on inverse transport theory

1. G. Bal and F. Monard, Inverse transport with isotropic time-harmonic sources, to appear in SIAM Journal of Mathematical Analysis, 2012.
2. 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.
3. G. Bal and A. Jollivet, Time-dependent angularly averaged inverse transport, Inverse Problems, 25, 075010, 2009.
4. G. Bal and A. Jollivet, Stability estimates for time dependent inverse transport, SIAM J. Math. Anal., 42(2), pp. 679-700, 2010
5. 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

1. F. Monard and G. Bal, Inverse anisotropic diffusion from power density measurements in two dimensions, submitted to Inverse Problems, 2011.
2. F. Monard and G. Bal, Inverse diffusion problems with redundant internal information, submitted to Inverse Probl. Imaging, 2011.
3. G. Bal, Cauchy problem for Ultrasound Modulated EIT, submitted, 2011.
4. G. Bal, E. Bonnetier, F. Monard and F. Triki, Inverse diffusion from knowledge of power densities, submitted to Inverse Probl. Imaging, 2011.
5. G. Bal and K. Ren, On Multi-spectral quantitative photoacoustic tomography, submitted.
6. G. Bal and K. Ren, Multiple-source quantitative photoacoustic tomography, Inverse problems, 27(7), 075003, 2011.
7. G. Bal and K. Ren, Non-uniqueness result for a hybrid inverse problem , to appear in Contemporary Mathematics, 2012.
8. G. Bal, K. Ren, G. Uhlmann and T. Zhou, Quantitative Thermo-acoustics and related problems, Inverse Problems, 27(5), 055007, 2011.
9. G. Bal and J.C. Schotland, Inverse Scattering and Acousto-Optic Imaging, Phys. Rev. Letters, 104, 043902, 2010
10. G. Bal and G. Uhlmann, Inverse Diffusion Theory of Photoacoustics, Inverse Problems, 26(8), 085010, 2010
11. G. Bal, A. Jollivet and V. Jugnon, Inverse Transport Theory of Photoacoustics, Inverse Problems, 26, 025011, 2010

Articles on Numerical Methods for transport

1. 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

1. A. Jollivet, On inverse problems in electromagnetic field in classical mechanics at fixed energy, J. Geom. Anal. 17:(2), 275--319 (2007).
2. A. Jollivet, On inverse problems for the multidimensional relativistic Newton equation at fixed energy, Inverse Problems 23:(1), 231--242 (2007).
3. A. Jollivet, On inverse scattering for the multidimensional relativistic Newton equation at high energies, J. Math. Phys. 47:(6) 062902, (2006).