, As with previous simulations, we observe that the reconstruction of the source is much better by using the new position of the sensors. As for choosing a good initial position

H. Akhouayri, M. Bergounioux, A. Silva, P. Elbau, A. Litman et al., Quantitative thermoacoustic tomography with microwaves sources, Journal of Inverse and Ill Problems, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01267412

H. Ammari, An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume, SIAM J. Control Optim, vol.41, issue.4, pp.1194-1211, 2002.

H. Ammari, An introduction to mathematics of emerging biomedical imaging, 2008.

H. Ammari, E. Bossy, V. Jugnon, and H. Kang, Mathematical modeling in photoacoustic imaging of small absorbers, SIAM Rev, vol.52, issue.4, pp.677-695, 2010.

H. Ammari, E. Bretin, J. Garnier, and A. Wahab, Time reversal in attenuating acoustic media, Mathematical and statistical methods for imaging, vol.548, pp.151-163, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00660346

H. Ammari and H. Kang, Reconstruction of small inhomogeneities from boundary measurements. Number 1846, 2004.

S. R. Arridge, Optical tomography in medical imaging, Inverse Problems, vol.15, issue.2, 1999.

G. Bal, K. Ren, G. Uhlmann, and T. Zhou, Quantitative thermo-acoustics and related problems, Inverse Problems, vol.27, issue.5, p.15, 2011.

G. Bal and G. Uhlmann, Inverse diffusion theory of photoacoustics, Inverse Problems, vol.26, issue.8, p.20, 2010.

A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci, vol.2, issue.1, pp.183-202, 2009.

M. Bergounioux, X. Bonnefond, T. Haberkorn, and Y. Privat, An optimal control problem in photoacoustic tomography, Mathematical Models and Methods in Applied Sciences, vol.24, issue.12, pp.2525-2548, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00833867

X. Bonnefond, ContributionsàContributionsà la tomographie thermoacoustique. Modélisation et inversion, 2010.

E. Bretin, C. Lucas, and Y. Privat, A time reversal algorithm in acoustic media with dirac measure approximations, Inverse Problems, vol.34, issue.4, p.45004, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01529580

A. Chambolle, An algorithm for total variation minimization and applications, Special issue on mathematics and image analysis, vol.20, issue.1-2, pp.89-97, 2004.

D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences, 2013.

R. Dautray and J. Lions, Mathematical analysis and numerical methods for science and technology, vol.5, 1993.

E. Demidenko, A. Hartov, N. Soni, and K. D. Paulsen, On optimal current patterns for electrical impedance tomography, IEEE Transactions on Biomedical Engineering, vol.52, issue.2, pp.238-248, 2005.

I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, p.3600

, Market Street, Floor, vol.6, 1999.

L. C. Evans, Partial differential equations, volume 19 of Graduate Studies in Mathematics, 1998.

H. Garde and S. Staboulis, Convergence and regularization for monotonicitybased shape reconstruction in electrical impedance tomography, Numer. Math, vol.135, issue.4, pp.1221-1251, 2017.

Y. Hristova, Time reversal in thermoacoustic tomography-an error estimate, Inverse Problems, vol.25, issue.5, pp.55008-55022, 2009.

Y. Hristova, P. Kuchment, and L. Nguyen, Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media, Inverse Problems, vol.24, issue.5, p.25, 2008.

N. Hyvönen, A. Seppänen, and S. Staboulis, Optimizing electrode positions in electrical impedance tomography, SIAM J. Appl. Math, vol.74, issue.6, pp.1831-1851, 2014.

M. Neumayer, M. Flatscher, T. Bretterklieber, and S. Puttinger, Optimal design of ect sensors using prior knowledge, Journal of Physics: Conference Series, vol.1047, issue.1, p.12012, 2018.

S. K. Patch and O. Scherzer, Photo-and thermo-acoustic imaging introduction, verse Problems, vol.23, pp.1-10, 2017.

Y. Privat, E. Trélat, and E. Zuazua, Optimal location of controllers for the onedimensional wave equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.30, issue.6, pp.1097-1126, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00683556

Y. Privat, E. Trélat, and E. Zuazua, Optimal observation of the one-dimensional wave equation, J. Fourier Anal. Appl, vol.19, issue.3, pp.514-544, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00679577

Y. Privat, E. Trélat, and E. Zuazua, Complexity and regularity of maximal energy domains for the wave equation with fixed initial data, Discrete Contin. Dyn. Syst. Ser. A, vol.35, issue.12, pp.6133-6153, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00813647

Y. Privat, E. Trélat, and E. Zuazua, Optimal shape and location of sensors for parabolic equations with random initial data. Archive for Rational Mechanics and Analysis, vol.216, pp.921-981, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00965668

Y. Privat, E. Trélat, and E. Zuazua, Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains, J. Eur. Math. Soc. (JEMS), vol.18, issue.5, pp.1043-1111, 2016.

O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, and F. Lenzen, Variational Methods in Imaging, 2008.

A. Wirgin, The inverse crime, 13402.
URL : https://hal.archives-ouvertes.fr/hal-00001084

L. Xu and M. Wang, Photoacoustic imaging in biomedecine, Rev. Sci. Instrum, vol.77, issue.4, 2006.

W. Yan, S. Hong, and R. Chaoshi, Optimum design of electrode structure and parameters in electrical impedance tomography, Physiological Measurement, vol.27, issue.3, p.291, 2006.