FREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORS

This paper is concerned with a version of photoacoustic tomography, that uses line shaped detectors (instead of point-like ones) for the recording of acoustic data. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional ones. First, the initial data of the two-dimensional wave equation is recovered from boundary data, and second, the classical two-dimensional Radon transform is inverted. We discuss uniqueness and stability of reconstruction, and compare frequency domain reconstruction formulas for various geometries.

[1]  Otmar Scherzer,et al.  KACZMARZ METHODS FOR REGULARIZING NONLINEAR ILL-POSED EQUATIONS II: APPLICATIONS , 2007 .

[2]  Thomas Schuster,et al.  On a Regularization Scheme for Linear Operators in Distribution Spaces with an Application to the Spherical Radon Transform , 2005, SIAM J. Appl. Math..

[3]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[4]  Minghua Xu,et al.  Exact frequency-domain reconstruction for thermoacoustic tomography. II. Cylindrical geometry , 2002, IEEE Transactions on Medical Imaging.

[5]  V. Palamodov.  Reconstructive Integral Geometry , 2004 .

[6]  Heinz Schmidt-Kloiber,et al.  Light distribution measurements in absorbing materials by optical detection of laser‐induced stress waves , 1996 .

[7]  Stephen J. Norton,et al.  Ultrasonic Reflectivity Imaging in Three Dimensions: Exact Inverse Scattering Solutions for Plane, Cylindrical, and Spherical Apertures , 1981, IEEE Transactions on Biomedical Engineering.

[8]  Barbara Kaltenbacher,et al.  Iterative Regularization Methods for Nonlinear Ill-Posed Problems , 2008, Radon Series on Computational and Applied Mathematics.

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

[10]  L. Andersson.  On the determination of a function from spherical averages , 1988 .

[11]  K. P. Köstli,et al.  Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response. , 2003, Applied optics.

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

[13]  Peter Kuchment,et al.  On the injectivity of the circular Radon transform , 2005 .

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

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

[16]  Martin Frenz,et al.  Fourier reconstruction in optoacoustic imaging using truncated regularized inverse k-space interpolation , 2007 .

[17]  Stephen J. Norton,et al.  Reconstruction of a two‐dimensional reflecting medium over a circular domain: Exact solution , 1980 .

[18]  Massoud Motamedi,et al.  Optoacoustic technique for noninvasive monitoring of blood oxygenation: a feasibility study. , 2002, Applied optics.

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

[20]  Wiendelt Steenbergen,et al.  The Twente Photoacoustic Mammoscope: system overview and performance , 2005, Physics in medicine and biology.

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

[22]  Robert A. Kruger,et al.  Thermoacoustic Molecular Imaging of Small Animals , 2003 .

[23]  V. Palamodov,et al.  Reconstruction from limited data of arc means , 2000 .

[24]  Victor Palamodov.  Remarks on the general Funk-Radon transform and thermoacoustic tomography , 2007 .

[25]  Leonid Kunyansky.  A series solution and a fast algorithm for the inversion of the spherical mean Radon transform , 2007 .

[26]  J. Shewchuk.  An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[27]  Xu Xiao.  Photoacoustic imaging in biomedicine , 2008 .

[28]  Robert A Kruger,et al.  Thermoacoustic computed tomography using a conventional linear transducer array. , 2003, Medical physics.

[29]  Peter Kuchment,et al.  A Range Description for the Planar Circular Radon Transform , 2006, SIAM J. Math. Anal..

[30]  P. Burgholzer,et al.  Photoacoustic tomography using a fiber based Fabry-Perot interferometer as an integrating line detector and image reconstruction by model-based time reversal method , 2007, European Conference on Biomedical Optics.

[31]  Trace identities for solutions of the wave equation with initial data supported in a ball , 2005 .

[32]  P. Burgholzer,et al.  Thermoacoustic tomography with integrating area and line detectors , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[33]  Otmar Scherzer,et al.  Filtered backprojection for thermoacoustic computed tomography in spherical geometry , 2005, Mathematical Methods in the Applied Sciences.

[34]  A. Beltukov,et al.  Operator identities relating sonar and Radon transforms in Euclidean space , 2006, math/0607437.

[35]  E. T. Quinto,et al.  Range descriptions for the spherical mean Radon transform. I. Functions supported in a ball , 2006, math/0606314.

[36]  Edward Z. Zhang,et al.  Fabry Perot polymer film fibre-optic hydrophones and arrays for ultrasound field characterisation , 2004 .

[37]  S. Jacques,et al.  Iterative reconstruction algorithm for optoacoustic imaging. , 2002, The Journal of the Acoustical Society of America.

[38]  John A. Fawcett,et al.  Inversion of N-dimensional spherical averages , 1985 .

[39]  Mark A. Anastasio,et al.  Application of inverse source concepts to photoacoustic tomography , 2007 .

[40]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[41]  F. D. de Mul,et al.  Three-dimensional photoacoustic imaging of blood vessels in tissue. , 1998, Optics letters.

[42]  Alexander A. Oraevsky,et al.  Optoacoustic tomography of breast cancer with arc-array transducer , 2000, BiOS.

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

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

[45]  William Rundell,et al.  Surveys on solution methods for inverse problems , 2000 .

[46]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[47]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[48]  Markus Haltmeier,et al.  Inversion of Spherical Means and the Wave Equation in Even Dimensions , 2007, SIAM J. Appl. Math..

[49]  Yuan Xu,et al.  Rhesus monkey brain imaging through intact skull with thermoacoustic tomography , 2006, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[50]  Roy G. M. Kolkman,et al.  In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor , 2003 .

[51]  R. Kruger,et al.  Photoacoustic ultrasound (PAUS)--reconstruction tomography. , 1995, Medical physics.

[52]  Alexander G. Ramm.  Injectivity of the spherical means operator , 2002 .

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

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

[55]  Eric Todd Quinto,et al.  Injectivity Sets for the Radon Transform over Circles and Complete Systems of Radial Functions , 1996 .

[56]  Markus Haltmeier,et al.  Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors , 2007 .

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

[58]  Geng Ku,et al.  Deeply penetrating photoacoustic tomography in biological tissues enhanced with an optical contrast agent. , 2005, Optics letters.

[59]  Minghua Xu,et al.  Photoacoustic tomography of biological tissues with high cross-section resolution: reconstruction and experiment. , 2002, Medical physics.

[60]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[61]  Rakesh,et al.  The spherical mean value operator with centers on a sphere , 2007 .

[62]  L. Ehrenpreis.  The Universality of the Radon Transform , 2003 .

[63]  Jin Zhang,et al.  Half-time image reconstruction in thermoacoustic tomography , 2005, IEEE Transactions on Medical Imaging.

[64]  Rakesh,et al.  The range of the spherical mean value operator for functions supported in a ball , 2006 .

[65]  Otmar Scherzer,et al.  THERMOACOUSTIC TOMOGRAPHY AND THE CIRCULAR RADON TRANSFORM: EXACT INVERSION FORMULA , 2007 .

[66]  Otmar Scherzer,et al.  Thermoacoustic tomography using a fiber-based Fabry-Perot interferometer as an integrating line detector , 2006, SPIE BiOS.

[67]  Jin Zhang,et al.  Weighted expectation maximization reconstruction algorithms for thermoacoustic tomography , 2005, IEEE Transactions on Medical Imaging.

[68]  R. Kruger,et al.  Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434 MHz-feasibility study. , 2000, Radiology.

[69]  Markus Haltmeier,et al.  Photoacoustic tomography using a Mach-Zehnder interferometer as an acoustic line detector. , 2007, Applied optics.

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

[71]  H. Weber,et al.  Temporal backward projection of optoacoustic pressure transients using fourier transform methods. , 2001, Physics in medicine and biology.

[72]  M. Haltmeier,et al.  Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[73]  Michael V. Klibanov,et al.  The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium , 2007, SIAM J. Sci. Comput..

[74]  Markus Haltmeier,et al.  Three-dimensional photoacoustic tomography using acoustic line detectors , 2007, SPIE BiOS.

[75]  A. Oraevsky,et al.  Detection of ultrawide-band ultrasound pulses in optoacoustic tomography , 2003, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.