Geodesic
One dimensional inverse problem in photoacoustic. Numerical testing
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 140-149 
D. Langemann; A. S. Mikhaylov; V. S. Mikhaylov. One dimensional inverse problem in photoacoustic. Numerical testing. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 140-149. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a9/
@article{ZNSL_2018_471_a9,
     author = {D. Langemann and A. S. Mikhaylov and V. S. Mikhaylov},
     title = {One dimensional inverse problem in photoacoustic. {Numerical} testing},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--149},
     year = {2018},
     volume = {471},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a9/}
}
TY  - JOUR
AU  - D. Langemann
AU  - A. S. Mikhaylov
AU  - V. S. Mikhaylov
TI  - One dimensional inverse problem in photoacoustic. Numerical testing
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 140
EP  - 149
VL  - 471
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a9/
LA  - en
ID  - ZNSL_2018_471_a9
ER  - 
%0 Journal Article
%A D. Langemann
%A A. S. Mikhaylov
%A V. S. Mikhaylov
%T One dimensional inverse problem in photoacoustic. Numerical testing
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 140-149
%V 471
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a9/
%G en
%F ZNSL_2018_471_a9

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the problem of reconstruction of Cauchy data for the wave equation in $\mathbb R^1$ by the measurements of its solution on the boundary of the finite interval. This is a one-dimensional model for the multidimensional problem of photoacoustics, which was studied in [2]. We adapt and simplify the method for one-dimensional situation and provide the results on numerical testing to see the rate of convergence and stability of the procedure. We also give some hints on how the procedure of reconstruction can be simplified in 2d and 3d cases.

[1] S. A. Avdonin, S. A. Ivanov, Families of exponentials, Cambridge University Press, Cambridge, 1995 | MR | Zbl

[2] M. I. Belishev, D. Langemann, A. S. Mikhaylov, V. S. Mikhaylov, “On an inverse problem in photoacoustic”, J. Inverse and Ill-posed Problems (to appear)

[3] Minghua Xua, Lihong V. Wang, “Photoacoustic imaging in biomedicine”, Review Sci. Instruments, 77:4 (2006), 041101 | DOI

[4] P. Kuchment, L. Kunyansky, “Mathematics of thermoacoustic and photoacoustic tomography”, Handbook of Mathematical Methods in Imaging, v. 2, 2010, 817–866