Vector Field Tomography, an Overview

Computerized tomography usually deals with the determination of scalar quantities from integral information along lines. During the 90's tomographic methods have been developed that enable (at least partial) recovery also of vector elds from integral information. Depending on which component of the vector eld is considered, e.g. the ones parallel or transversal to the line, diierent characteristics of the ow can be reconstructed, e.g. the vorticity or the divergence. Using supplementary information, notably boundary conditions, complete reconstruction is possible in certain circumstances. Some important measuring principles are transmission time-of-ight and Doppler, either by acoustic or optic radiation. The paper overviews the basic mathematical results and application areas for vector eld tomography.

[1]  Kent Stråhlén A combinatorial approach to vector tomography for Doppler spectral data , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[2]  W. Munk,et al.  Observing the ocean in the 1990s , 1982, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[3]  Paul C. Lauterbur,et al.  On the Problem of Reconstructing Images of Non-Scalar Parameters from Projections. Application to Vector Fields , 1979, IEEE Transactions on Nuclear Science.

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

[5]  L. Desbat Eecient Parallel Sampling in Vector Eld Tomography , 1995 .

[6]  Laurent Desbat,et al.  Direct algebraic reconstruction and optimal sampling in vector field tomography , 1995, IEEE Trans. Signal Process..

[7]  V. Sharafutdinov Integral Geometry of Tensor Fields , 1994 .

[8]  H. Ermert,et al.  Phased array pulse Doppler tomography , 1991, IEEE 1991 Ultrasonics Symposium,.

[9]  N. Akhiezer,et al.  The Classical Moment Problem. , 1968 .

[11]  S J Norton,et al.  Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach. , 1982, Ultrasonic imaging.

[12]  Daniel Rouseff,et al.  A filtered backprojection method for the tomographic reconstruction of fluid vorticity , 1990 .

[13]  Kent Stråhlén Reconstructions from Doppler Radon transforms , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[14]  R L Byer,et al.  Three-dimensional beam-deflection optical tomography of a supersonic jet. , 1988, Applied optics.

[15]  Jerry L. Prince Convolution backprojection formulas for 3-D vector tomography with application to MRI , 1996, IEEE Trans. Image Process..

[16]  V. N. Kharchenko,et al.  TOMOGRAPHY OF ION AND ATOM VELOCITIES IN PLASMAS , 1995 .

[17]  Hillar Aben,et al.  Photoelastic tomography for three-dimensional flow birefringence studies , 1997 .

[18]  K. Stråhlén Some Integral Transforms of Vector Fields , 1996 .

[19]  Daniel Rouseff,et al.  Reconstruction of oceanic microstructure by tomography: A numerical feasibility study , 1991 .

[20]  Gunnar Sparr,et al.  Doppler tomography for vector fields , 1995 .

[21]  Jerry L. Prince Tomographic reconstruction of 3-D vector fields using inner product probes , 1994, IEEE Trans. Image Process..

[22]  Robert C. Spindel,et al.  Ocean acoustic tomography: Mesoscale velocity , 1987 .

[23]  Stephen J. Norton Unique tomographic reconstruction of vector fields using boundary data , 1992, IEEE Trans. Image Process..

[24]  Integral geometry in projective space , 1970 .

[25]  Osamu Ikeda,et al.  Introduction of mass conservation law to improve the tomographic estimation of flow‐velocity distribution from differential time‐of‐flight data , 1985 .

[26]  Steven A. Johnson,et al.  RECONSTRUCTING THREE-DIMENSIONAL TEMPERATURE AND FLUID VELOCITY VECTOR FIELDS FROM ACOUSTIC TRANSMISSION MEASUREMENTS. , 1977 .

[27]  Hans Braun,et al.  Tomographic reconstruction of vector fields , 1991, IEEE Trans. Signal Process..

[28]  Ultrasound pulse Doppler tomography , 1988, IEEE 1988 Ultrasonics Symposium Proceedings..

[29]  Daniel Rouseff,et al.  Two-dimensional vector flow inversion by diffraction tomography , 1994 .

[30]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[31]  Markus Zahn,et al.  Transform relationship between Kerr-effect optical phase shift and nonuniform electric field distributions , 1994 .