Attenuation Models in Photoacoustics

The aim of this chapter is to review attenuation models in photoacoustic imaging and discuss their causality properties. We also derive integro-differential equations which the attenuated waves are satisfying and highlight the ill–conditionness of the inverse problem for calculating the unattenuated wave from the attenuated one, which has been discussed in Chap. 3.

[1]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[2]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[3]  F. John.  Partial differential equations , 1967 .

[4]  S. Lang,et al.  An Introduction to Fourier Analysis and Generalised Functions , 1959 .

[5]  A. Papoulis,et al.  The Fourier Integral and Its Applications , 1963 .

[6]  G. Braunss.  L. D. Landau und E. M. Lifschitz, Lehrbuch der Theoretischen Physik, Band VII, Elastizitätstheorie. (Übers. a. d. Russ.). VIII + 183 S. m. 28 Abb. Berlin 1965. Akademie‐Verlag. Preis geb. 16,– M , 1968 .

[7]  A. Tam.  Applications of photoacoustic sensing techniques , 1986 .

[8]  S. Webb.  The Physics of Medical Imaging , 1990 .

[9]  R. Waag,et al.  An equation for acoustic propagation in inhomogeneous media with relaxation losses , 1989 .

[10]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[11]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[12]  A. Welch,et al.  A review of the optical properties of biological tissues , 1990 .

[13]  Thomas L. Szabo,et al.  Time domain wave equations for lossy media obeying a frequency power law , 1994 .

[14]  Thomas L. Szabo,et al.  Causal theories and data for acoustic attenuation obeying a frequency power law , 1995 .

[15]  C. Gasquet,et al.  Fourier analysis and applications , 1998 .

[16]  I. Podlubny.  Fractional differential equations , 1998 .

[17]  Hughes,et al.  On a time-domain representation of the Kramers-Kronig dispersion relations , 2000, The Journal of the Acoustical Society of America.

[18]  Robert A. Kruger,et al.  Thermoacoustic CT: imaging principles , 2000, BiOS.

[19]  Yuan Xu,et al.  Exact frequency-domain reconstruction for thermoacoustic tomography. I. Planar geometry , 2002, IEEE Transactions on Medical Imaging.

[20]  Lihong V. Wang,et al.  Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain , 2003, Nature Biotechnology.

[21]  A. Hanyga,et al.  Power-law attenuation in acoustic and isotropic anelastic media , 2003 .

[22]  Minghua Xu,et al.  Time-domain reconstruction algorithms and numerical simulations for thermoacoustic tomography in various geometries , 2003, IEEE Transactions on Biomedical Engineering.

[23]  Rakesh,et al.  Determining a Function from Its Mean Values Over a Family of Spheres , 2004, SIAM J. Math. Anal..

[24]  Lihong V. Wang,et al.  Reconstructions in limited-view thermoacoustic tomography. , 2004, Medical physics.

[25]  S. Holm,et al.  Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency. , 2004, The Journal of the Acoustical Society of America.

[26]  Geng Ku,et al.  Multiple-bandwidth photoacoustic tomography. , 2004, Physics in medicine and biology.

[27]  N. V. Sushilov,et al.  Frequency-domain wave equation and its time-domain solutions in attenuating media. , 2004, The Journal of the Acoustical Society of America.

[28]  Otmar Scherzer,et al.  Thermoacoustic computed tomography with large planar receivers , 2004 .

[29]  J. Mobley,et al.  Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[30]  Lihong V. Wang,et al.  Universal back-projection algorithm for photoacoustic computed tomography. , 2005 .

[31]  Lihong V. Wang,et al.  Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging , 2006, Nature Biotechnology.

[32]  Lihong V. Wang,et al.  Photoacoustic imaging in biomedicine , 2006 .

[33]  Patrick J La Rivière,et al.  Image reconstruction in optoacoustic tomography for dispersive acoustic media. , 2006, Optics letters.

[34]  L. Kunyansky,et al.  Explicit inversion formulae for the spherical mean Radon transform , 2006, math/0609341.

[35]  M. Fenstermacher,et al.  First tests of molybdenum mirrors for ITER diagnostics in DIII-D divertor , 2006 .

[36]  Peter Kuchment,et al.  Mathematics of thermoacoustic and photoacoustic tomography , 2007 .

[37]  M. Haltmeier,et al.  Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors , 2007 .

[38]  Robert Nuster,et al.  Compensation of acoustic attenuation for high-resolution photoacoustic imaging with line detectors , 2007, SPIE BiOS.

[39]  Peter Kuchment,et al.  Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed , 2007, 0706.0598.

[40]  Paul C. Beard,et al.  Three-dimensional photoacoustic imaging of vascular anatomy in small animals using an optical detection system , 2007, SPIE BiOS.

[41]  Peter Kuchment,et al.  Mathematics of thermoacoustic tomography , 2007, European Journal of Applied Mathematics.

[42]  Linh V. Nguyen,et al.  Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media , 2008 .

[43]  Lihong V. Wang,et al.  Prospects of photoacoustic tomography. , 2008, Medical physics.

[44]  Otmar Scherzer,et al.  Variational Regularization Methods for the Solution of Inverse Problems , 2009 .

[45]  Vasilis Ntziachristos,et al.  Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo , 2009 .

[46]  P. Burgholzer,et al.  Image reconstruction in photoacoustic tomography using integrating detectors accounting for frequency-dependent attenuation , 2010, BiOS.

[47]  Alexander A. Oraevsky,et al.  Photons Plus Ultrasound: Imaging and Sensing , 2010 .

[48]  Otmar Scherzer,et al.  Causality analysis of frequency-dependent wave attenuation , 2011 .

[49]  E. Beltrami,et al.  Distributions and the Boundary Values of Analytic Functions , 2014 .