S. Giovanni, H. Alberti, and . Ammari, Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging, Applied and Computational Harmonic Analysis, 2015.

S. Giovanni, H. Alberti, B. Ammari, J. Jin, W. Seo et al., The linearized inverse problem in multifrequency electrical impedance tomography, SIAM Journal on Imaging Sciences, vol.9, issue.4, pp.1525-1551, 2016.

S. Giovanni, H. Alberti, F. Ammari, T. Romero, and . Wintz, Mathematical analysis of ultrafast ultrasound imaging, SIAM Journal on Applied Mathematics, vol.77, issue.1, pp.1-25, 2017.

G. Allaire, Homogenization and Two-Scale Convergence, SIAM Journal on Mathematical Analysis, vol.23, issue.6, pp.1482-1518, 1992.
DOI : 10.1137/0523084

URL : https://hal.archives-ouvertes.fr/hal-01111805

H. Ammari, . Garnier, . Jing, . Kang, . Lim et al., Mathematical and Statistical Methods for Multistatic Imaging, Lecture Notes in Mathematics, vol.2098, 2013.
DOI : 10.1007/978-3-319-02585-8

URL : https://hal.archives-ouvertes.fr/hal-00934743

H. Ammari, J. Garnier, L. Giovangigli, W. Jing, and J. Seo, Spectroscopic imaging of a dilute cell suspension, Journal de Math??matiques Pures et Appliqu??es, vol.105, issue.5, pp.603-661, 2016.
DOI : 10.1016/j.matpur.2015.11.009

URL : https://hal.archives-ouvertes.fr/hal-01377780

H. Ammari, L. Giovangigli, H. Kwon, J. Seo, and T. Wintz, Spectroscopic conductivity imaging of a cell culture, Asymptotic Analysis, vol.18, issue.2, pp.87-109, 2016.
DOI : 10.1155/2013/353849

URL : http://content.iospress.com/download/asymptotic-analysis/asy1387?id=asymptotic-analysis%2Fasy1387

H. Ammari and H. Kang, Reconstruction of small inhomogeneities from boundary measurements, 2004.
DOI : 10.1007/b98245

H. Ammari and H. Kang, Polarization and moment tensors: with applications to inverse problems and effective medium theory, 2007.

, BIBLIOGRAPHY

H. Ammari, F. Romero, and C. Shi, A signal separation technique for sub-cellular imaging using dynamic optical coherence tomography . To appear in Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017.

T. Bendory, Robust recovery of positive stream of pulses. arXiv preprint, 2015.

J. Bercoff, G. Montaldo, T. Loupas, D. Savery, F. Meziere et al., Ultrafast compound doppler imaging: providing full blood flow characterization, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.58, issue.1, pp.134-147, 2011.
DOI : 10.1109/TUFFC.2011.1780

J. Bercoff, G. Montaldo, T. Loupas, D. Savery, F. Mézière et al., Ultrafast compound doppler imaging: providing full blood flow characterization, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.58, issue.1, 2011.
DOI : 10.1109/TUFFC.2011.1780

S. Bjaerum, H. Torp, and K. Kristoffersen, Clutter filter design for ultrasound color flow imaging, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.49, issue.2, pp.204-216, 2002.
DOI : 10.1109/58.985705

A. Van-den-bos, The multivariate complex normal distribution-a generalization, IEEE Transactions on Information Theory, vol.41, issue.2, pp.537-539, 1995.
DOI : 10.1109/18.370165

N. Boyd, G. Schiebinger, and B. Recht, The alternating descent conditional gradient method for sparse inverse problems, Computational Advances in Multi-Sensor Adaptive Processing (CAM- SAP), 2015 IEEE 6th International Workshop on, pp.57-60, 2015.

C. Bruneel, R. Torguet, K. M. Rouvaen, E. Bridoux, and B. Nongaillard, Ultrafast echotomographic system using optical processing of ultrasonic signals, Applied Physics Letters, vol.19, issue.8, pp.371-373, 1977.
DOI : 10.1109/T-SU.1972.29698

J. Emmanuel, C. Candès, and . Fernandez-granda, Towards a mathematical theory of super-resolution, Communications on Pure and Applied Mathematics, vol.67, issue.6, pp.906-956, 2014.

C. G. and C. , The mechanics of the circulation, 2012.

T. Chang and K. Lee, Spectral properties of the layer potentials on lipschitz domains, Illinois Journal of Mathematics, vol.52, issue.2, pp.463-472, 2008.
DOI : 10.1007/s00229-009-0292-1

W. Cho and C. , Waves and fields in inhomogeneous media, 1995.

Y. De, C. , and F. Gamboa, Exact reconstruction using beurling minimal extrapolation, Journal of Mathematical Analysis and applications, vol.395, issue.1, pp.336-354, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00678423

C. Demene, T. Deffieux, M. Pernot, B. Osmanski, V. Biran et al., Spatiotemporal Clutter Filtering of Ultrafast Ultrasound Data Highly Increases Doppler and fUltrasound Sensitivity, IEEE Transactions on Medical Imaging, vol.34, issue.11, pp.342271-2285, 2015.
DOI : 10.1109/TMI.2015.2428634

URL : https://hal.archives-ouvertes.fr/hal-01541361

Q. Denoyelle, V. Duval, and G. Peyré, Support Recovery for Sparse Super-Resolution of Positive Measures, Journal of Fourier Analysis and Applications, vol.58, issue.3, pp.1-42, 2016.
DOI : 10.1109/TAP.1986.1143830

URL : https://hal.archives-ouvertes.fr/hal-01270184

Y. Desailly, O. Couture, M. Fink, and M. Tanter, Sono-activated ultrasound localization microscopy, Applied Physics Letters, vol.103, issue.17, p.174107, 2013.
DOI : 10.1109/TMI.2013.2255310

C. Errico, J. Pierre, S. Pezet, Y. Desailly, Z. Lenkei et al., Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging, Nature, vol.8, issue.7579, pp.499-502, 2015.
DOI : 10.1038/nmeth.1641

C. Errico, J. Pierre, S. Pezet, Y. Desailly, Z. Lenkei et al., Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging, Nature, vol.8, issue.7579, pp.527499-502, 2015.
DOI : 10.1038/nmeth.1641

E. B. Fabes, M. Sand, and J. K. Seo, The spectral radius of the classical layer potentials on convex domains, partial differential equations with minimal smoothness and applications, Math. Appl, vol.42, pp.129-137, 1992.

J. Gennisson, T. Deffieux, M. Fink, and M. Tanter, Ultrasound elastography: Principles and techniques. Diagnostic and Interventional Imaging, pp.487-495, 2013.

, BIBLIOGRAPHY

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-266, 2012.
DOI : 10.1515/jnum-2012-0013

URL : https://hal.archives-ouvertes.fr/hal-01476313

T. Samuel, . Hess, P. Thanu, . Girirajan, D. Michael et al., Ultrahigh resolution imaging by fluorescence photoactivation localization microscopy, Biophysical journal, vol.91, issue.11, pp.4258-4272, 2006.

K. Iizuka and P. Kmtky, Data adaptive signal estimation by singular value decomposition of data matrix, Proceedings of the IEEE, 1982.

C. Joo, C. Evans, T. Stepinac, T. Hasan, and J. De-boer, Diffusive and directional intracellular dynamics measured by field-based dynamic light scattering, Optics Express, vol.18, issue.3, pp.2858-2871, 2010.
DOI : 10.1364/OE.18.002858

J. Jossinet and . Lavandier, The phenomenology of acousto-electric interaction signals in aqueous solutions of electrolytes, Ultrasonics, vol.36, issue.1-5, pp.607-613, 1998.
DOI : 10.1016/S0041-624X(97)00113-3

A. Khelifi and H. Zribi, Asymptotic expansions for the voltage potentials with two-dimensional and three-dimensional thin interfaces, Mathematical Methods in the Applied Sciences, vol.81, issue.11, pp.2274-2290, 2011.
DOI : 10.1007/b98245

S. Kim, E. J. Lee, E. J. Woo, and J. K. Seo, Asymptotic analysis of the membrane structure to sensitivity of frequency-difference electrical impedance tomography, Inverse Problems, vol.28, issue.7, p.2012
DOI : 10.1088/0266-5611/28/7/075004

J. Laudereau, A. Grabar, M. Tanter, J. Gennisson, and F. Ramaz, Ultrafast acousto-optic imaging with ultrasonic plane waves, Optics Express, vol.24, issue.4, pp.3774-3789, 2016.
DOI : 10.1364/OE.24.003774

URL : https://hal.archives-ouvertes.fr/hal-01297520

S. Link, A. Mostafa, and . El-sayed, Shape and size dependence of radiative, non-radiative and photothermal properties of gold nanocrystals, International Reviews in Physical Chemistry, vol.19, issue.3, pp.409-453, 2000.
DOI : 10.1080/01442350050034180

E. Mace, G. Montaldo, B. F. Osmanski, I. Cohen, M. Fink et al., Figure 8, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.60, issue.3, pp.492-506, 2013.
DOI : 10.1109/TUFFC.2013.2592/mm4

E. Mace, G. Montaldo, I. Cohen, M. Baulac, M. Fink et al., Functional ultrasound imaging of the brain, Nature Methods, vol.12, issue.8, pp.662-664, 2011.
DOI : 10.1038/nmeth.1530

A. Manduca, E. Travis, M. Oliphant, . Dresner, . Mahowald et al., Magnetic resonance elastography: Non-invasive mapping of tissue elasticity, Medical Image Analysis, vol.5, issue.4, pp.237-254, 2001.
DOI : 10.1016/S1361-8415(00)00039-6

J. Mansour, Biomechanics of cartilage Kinesiology: the mechanics and pathomechanics of human movement, pp.66-79, 2003.

W. Graeme and . Milton, The theory of composites, 2002.

G. Montaldo, M. Tanter, J. Bercoff, N. Benech, and M. Fink, Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.56, issue.3, pp.489-506, 2009.
DOI : 10.1109/TUFFC.2009.1067

G. Nguestseng, A General Convergence Result for a Functional Related to the Theory of Homogenization, SIAM Journal on Mathematical Analysis, vol.20, issue.3, pp.608-623, 1989.
DOI : 10.1137/0520043

J. Nédélec, Acoustic and electromagnetic equations: integral representations for harmonic problems, 2001.

J. Bradley and . Roth, The role of magnetic forces in biology and medicine, Experimental Biology and Medicine, vol.236, issue.2, pp.132-137, 2011.

K. Kirk and S. , Diagnostic ultrasound: Imaging and blood flow measurements, 2015.

L. Thomas and . Szabo, Diagnostic Ultrasound Imaging: Inside Out, 2014.

M. Tanter and M. Fink, Ultrafast imaging in biomedical ultrasound, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol.61, issue.1, pp.102-119, 2014.
DOI : 10.1109/TUFFC.2014.2882

URL : https://doi.org/10.1109/tuffc.2014.6689779

A. Michael, . Thompson, D. Matthew, W. Lew, and . Moerner, Extending microscopic resolution with single-molecule imaging and active control. Annual review of biophysics, pp.321-342, 2012.

K. Watanabe, Integral transform techniques for Green's function, volume 76 of Lecture Notes in Applied and Computational Mechanics, 2015.