Photoacoustic imaging for attenuating acoustic media

Lecture Notes in Mathematics

Volumn 2035, Issue , 2012, Pages 57-84

  Ammari, Habib ^a   Bretin, Elie ^b   Jugnon, Vincent ^a   Wahab, Abdul ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80053654604     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-22990-9_3     Document Type: Article

References (33)

1. H. Ammari, M. Asch, L. Guadarrama Bustos, V. Jugnon, H. Kang, Transient wave imaging with limited-view data, SIAM J. Imag. Sci, to appear.
2. H. Ammari, E. Bossy, V. Jugnon, H. Kang, Mathematical modelling in photoacoustic imaging of small absorbers, SIAM Rev. 52, 677-695 (2010)
3. H. Ammari, E. Bossy, V. Jugnon, H. Kang, Quantitative photo-acoustic imaging of small absorbers, SIAM J. Appl. Math. 71, 676-693 (2011)
4. H. Ammari, E. Bretin, J. Garnier, V. Jugnon, Coherent interferometric algorithms for photoacoustic imaging, SIAM J. Numer. Anal., to appear.
5. C. Bardos, G. Lebeau, J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Contr. Optim. 30, 1024-1065 (1992) (Pubitemid 23572519)
6. A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci. 2, 183-202 (2009)
7. P. Burgholzer, H. Grün, M. Haltmeier, R. Nuster, G. Paltauf, Compensation of acoustic attenuation for high resolution photoacoustic imaging with line detectors, Proc. of SPIE, 6437, 643724 (2007)
8. A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imag. Vis. 20, 89-97 (2004)
9. W. Chen, S. Holm, Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency, J. Acoust. Soc. Amer. 115, 1424-1430 (2004) (Pubitemid 38451295)
10. P. Combettes, V.Wajs, Signal recovery by proximal forward-backward splitting, Mult. Model. Simul. 4, 1168-1200 (2005) (Pubitemid 44932287)
11. B.T. Cox, J.G. Laufer, P.C. Beard, The challenges for quantitative photoacoustic imaging, Proc. of SPIE 7177, 717713 (2009)
12. I. Daubechies, M. Defrise, C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. 57, 1413-1457 (2004) (Pubitemid 39427442)
13. D. Finch, M. Haltmeier, Rakesh, Inversion of spherical means and the wave equation in even dimensions, SIAM J. Appl. Math. 68, 392-412 (2007) (Pubitemid 351584838)
14. D. Finch, S. Patch, Rakesh, Determining a function from its mean-values over a family of spheres, SIAM J. Math. Anal. 35, 1213-1240 (2004) (Pubitemid 39288774)
15. M. Haltmeier, R. Kowar, A. Leitao, O. Scherzer, Kaczmarz methods for regularizing nonlinear ill-posed equations II: Applications, Inverse Probl. Imag. 1, 507-523 (2007)
16. M. Haltmeier, T. Schuster, O. Scherzer, Filtered backprojection for thermoacoustic computed tomography in spherical geometry, Math. Meth. Appl. Sci. 28, 1919-1937 (2005) (Pubitemid 41495247)
17. M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, G. Paltauf, Thermoacoustic tomography and the circular Radon transform: exact inversion formula, Math. Model. Meth. Appl. Sci. 17(4), 635-655 (2007)
18. L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis, Classics in Mathematics, Springer, Berlin (2003)
19. R. Kowar, Integral equation models for thermoacoustic imaging of dissipative tissue, Inverse Probl. 26, 095005 (18pp) (2010)
20. R. Kowar, O. Scherzer, X. Bonnefond, Causality analysis of frequency dependent wave attenuation, Math. Meth. Appl. Sci. 34, 108-124 (2011)
21. P. Kuchment, L. Kunyansky, in Mathematics of Photoacoustics and Thermoacoustic Tomography, ed. by O. Scherzer. Handbook of Mathematical Methods in Imaging (Springer, New York, 2011)
22. P. Kunchment, L. Kunyansky, Mathematics of thermoacoustic tomography, Europ. J. Appl. Math. 19, 191-224 (2008)
23. L. Kunyansky, Explicit inversion formulas for the spherical mean Radon transform, Inverse Probl. 23, 373-383 (2007) (Pubitemid 46485861)
24. P.J. La Rivière, J. Zhang, M.A. Anastasio, Image reconstruction in optoacoustic tomography for dispersive acoustic media, Opt. Lett. 31, 781-783 (2006)
25. K. Maslov, H.F. Zhang, L.V. Wang, Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo, Inverse Probl. 23, S113-S122 (2007) (Pubitemid 350212328)
26. L.V. Nguyen, A family of inversion formulas in thermoacoustic tomography, Inverse Probl. Imag. 3, 649-675 (2009)
27. K. Patch, M. Haltmeier, Thermoacoustic tomography - ultrasound attenuation artifacts, IEEE Nucl. Sci. Symp. Conf. 4, 2604-2606 (2006)
28. N.V. Sushilov, R.S.C. Cobbold, Frequency-domain wave equation and its timedomain solutions in attenuating media, J. Acoust. Soc. Am. 115, 1431-1436 (2004) (Pubitemid 38451296)
29. T.L. Szabo. Causal theories and data for acoustic attenuation obeying a frequency power law. J. Acoust. Soc. Am. 97, 14-24 (1995)
30. B.E. Treeby, B.T. Cox, Fast, tissue-realistic models of photoacoustic wave propagation for homogeneous attenuating media, Proc. of SPIE 7177, 717716 (2009)
31. L.V. Wang, X. Yang, Boundary conditions in photoacoustic tomography and image reconstruction, J. Biomed. Optic. 12, 014027 (2007)
32. M. Xu, L.V.Wang, Photoacoustic imaging in biomedicine, Rev. Scient. Instrum. 77, 041101 (2006)
33. Y. Xu, L.V.Wang, Reconstructions in limited-view thermoacoustic tomography, Med. Phys. 31, 724-733 (2004) (Pubitemid 38508852)