Acoustical Imaging pp 379-431 | Cite as

# Ultrasonic Imaging by Reconstructive Tomography

## Abstract

The recent development of X-ray computer reconstructive tomography has brought about a revolution in radiology. It has given the practicing physician a new degree of access to what is going on inside a patient’s body. The computer has become an important factor for implementing diagnostic techniques in the major hospitals of the world. In recognition of this fact, G.N. Hounsfield and A.M. Cormack were made co-recipients of the 1979 Nobel Award in physiology and medicine.

In conventional radiology, X rays diverge from a single source to project onto film a shadowgraph of the structure along the paths of the rays. But structural elements, cleanly separated in the three-dimensional object, often overlap in the final two-dimensional image in such a way as to make them hard to distinguish. This is particularly true of structural elements of similar density.

In reconstructive tomography there is no overlap. An image is computed from a large number of projections. The image has the form of a two-dimensional mapping of the discrete non-overlapping structural elements in a single plane of the body. Ordinary X-ray technology is combined with sophisticated computer processing to make this possible.

The X-ray source and detector move around the body, and in effect, hundreds of X-ray pictures are made. Instead of being recorded on film, the information is sent to a computer to be processed by it in making a tomogram. With this approach it is possible in principle to obtain the image of any cross section within the body. The technique has proven to be invaluable for the diagnosis of brain tumors and many other pathologies.

However, it has one disadvantage: it is invasive. It depends on ionizing radiation. Too much exposure to X rays will harm the patient.

But X rays are not the only kind of radiation for which reconstructive tomography is feasible. Microwaves, electron beams, ultrasound, fast subatomic particles from accelerators, gamma rays from such sources are positron annihilation, and even magnetic fields can be used. Ultrasound is particularly attractive in reconstructive tomography, and that is what this paper is all about.

Acoustic energy can often give a view of a cross section not available with X rays or other types of radiation. A mapping of acoustic and elastic variations can be expected to provide a basically different pattern than a mapping of variations in X-ray absorption and scattering coefficients. In addition, a mapping of one kind of acoustic parameter will yield quite a different picture than that of another. So far, two acoustic parameters have received the most attention in research: acoustic attenuation and acoustic refractive index. Mappings of variations in either parameter require transmitting the ultrasound through the object. But ultrasound can also be reflected from objects. Inhomogeneities within an object provide echoes and research is going on to produce mappings of variations in ultrasonic reflection. Thus, computer-assisted acoustic-echo tomography is being examined and also tomographic extensions of Doppler processing.

In reconstructive tomography it is essential to know the paths taken by the rays in going from source to detector. With X rays the paths are all essentially straight and therefore easy to take into account. This is not the case with ultrasound. When an ultrasonic beam propagates through an object, it undergoes deflection (refraction and reflection) at almost every interface between regions of different refractive index. Diffraction of the acoustic waves also occurs. Because of the wavelength differences between X rays and ultrasound, diffraction is far more important for ultrasound than for X rays. Thus refraction, reflection and diffraction are special problems peculiar to ultrasonic reconstructive tomography.

## Keywords

Residual Stress Reconstructive Tomography Velocity Variation Ultrasonic Imaging Computer Assisted Tomography## Preview

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## References & Bibliography

- A68.H.O. Anger, “Tomographic gamma-ray scanner with simultaneous readout of several planes,” in Fundamental Problems in Scanning, Eds. A. Gottschalk, R.N. Beck, Springfield, Illinois: Thomas, 1968, pp. 195–211.Google Scholar
- A76a.R.E. Alvarez and A. Macovski, “Energy-selective reconstructions in X-ray computerized tomography,” Phys. Med. Biol., vol. 21, pp. 733–744, 1976.CrossRefGoogle Scholar
- A76b.R.E. Alvarez and A. Macovski, “Noise and dose in energy dependence computerized tomography,” Proc. SPIE, vol. 96, pp. 131–137, 1976.ADSGoogle Scholar
- A77.H.C. Andrews and B.R. Hunt, Digital Image Restoration, Englewood Cliffs, New Jersey: Prentice Hall, 1977.Google Scholar
- B56.R.N. Bracewell, “Strip integration in radioastronomy,” Aust. J. Phys., vol. 9, pp. 198–217, 1956.MathSciNetADSMATHCrossRefGoogle Scholar
- B61.R.N. Bracewell and G. Swarup, “The Stanford microwave spectroheliograph antenna, a microsteradian pencil-beam interferometer,” Trans. I.R.E., vol. AP-9, pp. 22–30, January 1961.Google Scholar
- B67.R.N. Bracewell and A.C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J., vol. 150, pp. 427–434, November 1967.ADSCrossRefGoogle Scholar
- B70a.R. Bender, et. al., “ART and the ribosome: A preliminary report on the three-dimensional structure of individual ribosomes determined by an algebraic reconstruction technique,” J. Theor. Biol. vol. 29, pp. 483–487, 1970.CrossRefGoogle Scholar
- B70b.M.V. Berry and D.F. Gibbs, “The interpretation of optical projections,” Proc. Roy. Soc. Lond. A., vol. 314, pp. 143–152, January 6, 1970.ADSCrossRefGoogle Scholar
- B71a.R.H.T. Bates and T.M. Peters, “Towards improvements in tomography,” New Zealand J. Sci., vol. 14, pp. 883–896, 1971.Google Scholar
- B71b.S.H. Bellman, R. Bender, R. Gordon, and J.E. Rowe, “ART is science, being a defense of algebraic reconstruction techniques for three-dimensional electron microscopy,” J. Theor. Biol., vol. 32, pp. 205–216, 1971.CrossRefGoogle Scholar
- B73.G.L. Brownell and C.A. Burnham, “MGH positron camera,” in Tomographic Imaging in Nuclear Medicine, G.S. Freedman, Ed., Soc. Nucl. Med., 1973, p. 154.Google Scholar
- B74.T.F. Budinger and G.T. Gullberg, “Three dimensional reconstruction of isotope distributions,” Phys. Med. Biol., vol. 19, pp. 387–389, 1974.CrossRefGoogle Scholar
- B76a.N.A. Baily and R.A. Keller, “A physical comparison of a fluoroscopic CAT system and the EMI head scanner,” Proc. SPIE, vol. 96, pp. 210–215, 1976.ADSGoogle Scholar
- B76b.N.A. Baily, R.A. Keller, C.V. Jakowatz, and A.C. Kak, “The capability of fluoroscopic systems for the production of computerized axial tomograms,” Investigative Radiology, vol. 11, pp. 434–439, Sept.-Oct. 1976.CrossRefGoogle Scholar
- B76c.R.A. Brooks and G. DiChiro, “Beam hardening in X-ray reconstructive tomography,” Phys. Med. Biol., vol. 21, pp. 390–398, 1976.CrossRefGoogle Scholar
- B76d.R.A. Brooks and G. DiChiro, “Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging,” Phys. Med. Biol., vol. 21, pp. 689–732, 1976.CrossRefGoogle Scholar
- B76e.R.A. Brooks and G. DiChiro, “Statistical limitations in X-ray reconstructive tomography,” Med. Phys., vol. 3, pp. 237–270, 1976.CrossRefGoogle Scholar
- B76f.R.A. Brooks and G.H. Weiss, “Interpolation problems in image reconstruction,” Proc. SPIE, vol. 96, pp. 313–319, 1976.Google Scholar
- B76g.T.F, Budinger and G.T. Gullberg, “Transverse section reconstruction of gamma-ray emitting radionuclides in patients,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, Ter Pogossian et al., Eds. Baltimore, MD: University Park Press, 1976.Google Scholar
- B77a.N.A. Baily, “Computerized tomography using video techniques,” Opt. Eng., vol. 16, pp. 23–27, Jan.–Feb. 1977.Google Scholar
- B77b.R.N. Bracewell, “Correction for collimator width (restoration) in reconstructive X-ray tomography,” J. Comput. Assist. Tomog., vol. 1, pp. 6–15, Jan. 1977.CrossRefGoogle Scholar
- B77c.R.A. Brooks, “A quantitative theory of the Hounsfield unit and its application to dual energy scanning,” J. Compt. Assist. Tomog., vol. 1, pp. 487–493, 1977.CrossRefGoogle Scholar
- B77d.R.A. Brooks and G. DiChiro, “Slice geometry in computer assisted tomography,” J. Compt. Assist. Tomog., vol. 1, pp. 191–199, 1977.CrossRefGoogle Scholar
- B77e.T.F. Budinger, S.E. Derenzo, G.T. Gullber, W.L. Greenber, and R.H. Huesman, “Emission computer assisted tomography with single photon and positron annihilation photon emitters,” J. Compt. Assist. Tomog., vol. 1, pp. 131–145, 1977.CrossRefGoogle Scholar
- B78a.C. Bohm, L. Eriksson, M. Bergstrom, J. Litton, R. Sundman, and M. Singh, “A computer assisted ringdetector positron camera system for reconstruction tomography of the brain,” IEEE Trans. Nucl. Sci., vol. NS-25, pp. 624–637, 1978.ADSCrossRefGoogle Scholar
- B78b.R.A. Brooks and G. DiChiro, “Split-detector computer tomography: A preliminary report,” Radiology, vol. 126, pp. 255–257, Jan. 1978.Google Scholar
- B78c.R.A. Brooks, G.H. Weiss, and A.J. Talbert, “A new approach to interpolation in computed tomography,” J. Compt. Assist. Tomog., vol. 2, pp. 577–585, Nov. 1978.CrossRefGoogle Scholar
- B78d.G.L. Brownell and S. Cochavi, “Transverse section imaging with carbon-11 labeled carbon monoxide, ” J. Compt. Assist. Tomog., vol. 2, pp. 533–538, Nov. 1978.CrossRefGoogle Scholar
- B80.J.S. Ball, S.A. Johnson, and F. Stanger, “Explicit inversion of the Helmholtz equation for ultrasound insonification and spherical detection,” this volume pp. 533–538, 1980.Google Scholar
- C63.A.M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys., vol. 34, no. 9, pp. 2722–2727, September 1963.ADSMATHCrossRefGoogle Scholar
- C64.A.M. Cormack, “Representation of a function by its line integrals with some radiological applications, II,” J. Appl. Phys., vol. 35, pp. 2908–2913, October 1964.ADSMATHCrossRefGoogle Scholar
- C69.L.A. Chernov, Wave Propagation in a Random Medium, New York: McGraw-Hill, 1969.Google Scholar
- C76a.P.L. Carson, T.V. Oughton and W.R. Hendee, “Ultrasonic transaxial tomography by reconstruction,” Ultrasound in Medicine, vol. 2, Eds. D. White and R. Barns, New York: Plenum Press, pp. 341–350, 1976.Google Scholar
- C76b.P.L. Carson, T.V. Oughton, and W.R. Hendee, “Ultrasound transaxial tomography by reconstruction,” in Ultrasound in Medicine, vol. 2, D.N. White and R.W. Barnes, Eds. New York: lenum Press, pp. 391–400, 1976.CrossRefGoogle Scholar
- C76c.Z.H. Cho, L. Eriksson, And J. Chan, “A circular ring transverse axial positron camera,” in Reconstruction Tomography in Diagnostic Radiology and Medicine, M.M. TerPogossian et al., Ed. Baltimore, MD: University Park Press, pp. 393–421, 1976.Google Scholar
- C77a.P.L. Carson, T.V. Oughton, W.R. Hendee, and A.S. Ahuja, “Imaging soft tissue through bone with ultrasound transmission tomography by reconstruction,” Med. Phys., vol. 4, pp. 302–309, July/Aug. 1977.CrossRefGoogle Scholar
- C77b.D.A. Chesler, S.J. Riederer, and N.J. Pelc, “Noise due to photon counting statistics in computed X-ray tomography,” J. Compt. Assist. Tomog., pp. 64–74, vol. 1, Jan. 1977.CrossRefGoogle Scholar
- C77c.Z.H. Cho, M.B. Cohen, M. Singh, L. Eriksson, J. Chan, N. MacDonald, and L. Spotter, “Performance and evaluation of the circular ring transverse axial positron camera,” IEEE Trans. Nucl. Sci., vol. NS-24, pp. 532–543, 1977.ADSCrossRefGoogle Scholar
- C77d.G. Chu and K.C. Tam, “Three dimensional imaging in the positron camera using Fourier techniques,” Phy. Med. Biol., vol. 22, pp. 245–265, 1977.CrossRefGoogle Scholar
- C78a.L.R. Carroll, “Design and performance characteristics of a production model positron imaging system,” IEEE Trans. Nucl. Sci., vol. NS-25, pp. 606–614, Feb. 1978.ADSCrossRefGoogle Scholar
- C78b.P.L. Carson, D.E. Dick, G.A. Thieme, M.L. Dick, E.J. Bayly, T.V. Oughton, G.L. Dubuque, and H.P. Bay, “Initial investigation of computed tomography for breast imaging with focused ultrasound beams,” Ultrasound in Medicine, vol. 4, D.N. White and E.A. Lyons, Eds. New York: Plenum Press, pp. 319–322, 1978.CrossRefGoogle Scholar
- C78c.L.T. Chang, “A method for attenuation correction in radionuclide computed tomography,” IEEE Trans. Nucl. Sci., vol. NS-25, pp. 638–643, Feb. 1978.ADSCrossRefGoogle Scholar
- C78d.R.C. Chase and J.A. Stein, “An improved image algorithm for CT scanners,” Med. Phy., vol. 5, pp. 497–499, Dec. 1978.CrossRefGoogle Scholar
- C78e.Z.H. Cho, O. Nalcioglu, and M.R. Furukhi, “Analysis of a cylindrical hybrid positron camera with Bismuth Germanate (BGO) scintillation crystals,” IEEE Trans. Nucl. Sci., vol. NS-25, pp. 952–963, Apr. 1978.ADSCrossRefGoogle Scholar
- C79a.P.L. Carson, A.L. Scherzinger, T.V. Oughton, J.E. Kubitschek, P.A. Lambert, G.E. Moore, M.G. Dunn, and D.E. Dick, “Progress in ultrasonic computed tomography (CT) of the breast,” SPIE Vol. 173, Application of Optical Instrumentation in Medicine VII, pp. 372–381, 1979.Google Scholar
- C79b.L.T. Chang, “Attenuation correction and incomplete projection in single photon emission computed tomography,” IEEE Trans. Nucl. Sci., vol. NS-25, Apr. 1979.Google Scholar
- C79c.C.R. Crawford and A.C. Kak, “Aliasing artifacts in CT images,” School Elec. Eng., Purdue Univ., West Lafayette, IN, Res. Rep. TR-EE 79-25, 1979.Google Scholar
- C80.T.R. Coulter, M. Kaveh, R.K. Mueller, and R.L. Rylander, “Experimental results with diffraction tomography,” to be published in the Proceedings of the 1979 Ultrasonics Symposium, 1980.Google Scholar
- D68.D.J. De Rosier and A. Klug, “Reconstruction of three-dimensional structures from electron micrographs,” Nature, vol. 217, pp. 130–134, January 13, 1968.ADSCrossRefGoogle Scholar
- D76a.K.A. Dines and A.C. Kak, “Measurement and reconstruction of ultrasonic parameters for diagnostic imaging,” School Elec. Eng., Purdue Univ., West Lafayette, IN, Res. Rep. TR-EE 77-4, Dec. 1976.Google Scholar
- D76b.P. Dreike and D.P. Boyd, “Convolution reconstruction of fan-beam reconstructions,” Comp. Graph. Image Process., pp. 459–469, vol. 5, 1976.CrossRefGoogle Scholar
- D77a.S.E. Derenzo, “Positron ring cameras for emission computed tomography,” IEEE Trans. Nucl. Sci., vol. NS-24, pp. 881–885, Apr. 1977.ADSCrossRefGoogle Scholar
- D77b.S.E. Derenzo, T.F. Budinger, J.L. Cahoon, R.H. Huesman, and H.G. Jackson, “High resolution computed tomography of positron emitter,” IEEE Trans. Nucl. Sci., col. NS-24, pp. 544–558, Feb. 1977.Google Scholar
- D78a.G. DiChiro, R.A. Brooks, L. Dubai, and E. Chew, “The apical artifact: Elevated attenuation values toward the apex of the skull,” J. Compt. Assist. Tomog., vol. 2, pp. 65–79, Jan. 1978.CrossRefGoogle Scholar
- D78b.A.J. Duerinckx and A. Macovski, “Polychromatic streak artifacts in computed tomography images,” J. Compt. Assist. Tomog., vol. 2, pp. 481–487, Sept. 1978.CrossRefGoogle Scholar
- D79.K.A. Dines and A.C. Kak, “Ultrasonic attenuation tomography of soft biological tissues,” Ultrasonic Imaging, vol. 1, pp. 16–33, Jan. 1979.CrossRefGoogle Scholar
- E66.E.R. Epp and H. Weiss, “Experimental study of the photon energy spectrum of primary diagnostic X-rays,” Phys. Med. Biol., vol. 11 pp. 225–238, 1966.CrossRefGoogle Scholar
- E76.L. Eriksson and Z.H. Cho, “A simple absortpion correction in positron (annihilation gamma coincidence detection) transverse axial tomography,” Phys. Med. Biol. vol. 21, pp. 429–433, 1976.CrossRefGoogle Scholar
- F78.E.J. Farrell, “Processing limitations of ultrasonic image reconstruction,” in Proc. 1978 Conf. Pattern Recognition and Image Processing, May 1978.Google Scholar
- G70.R. Gordon, R. Bender and G.T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol., vol. 29, pp. 471–481, December 1970.CrossRefGoogle Scholar
- G72.M. Goiten, “Three dimensional density reconstruction from a series of two dimensional projections,” Nucl. Instrum. Methods, vol. 101, pp. 509–518, 1972.ADSCrossRefGoogle Scholar
- G74.J.F. Greenleaf, S.A. Johnson, S.L. Lee, G.T. Herman, and E.H. Wood, “Algebraic reconstruction of spatial distribu tions of acoustic absorption within tissue from their two-dimensional acoustic projections,” in Acoustical Holography, vol. 5, Ed. P.S. Green, New York: Plenum Press, 1974, pp. 591–603.Google Scholar
- G75a.M. Gado and M. Phelps, “The peripheral zone of increased density in cranial computed tomography,” Radiology, vol. 117, pp. 71–74, 1975.Google Scholar
- G75b.R. Gordon, G.T. Herman and S.A. Johnson, “Image reconstruction from projections,” Scientific American, vol. 233, no. 4, pp. 56–68, October 1975.CrossRefGoogle Scholar
- G75c.J.F. Greenleaf, S.A. Johnson, W.F. Samayoa and F.A. Duck, (1975a) “Algebraic reconstruction of spatial distributions of acoustic velocities in tissue from their time-of-flight profiles,” in Acoustical Holography, vol. 6, N. Booth, Ed., New York: Plenum Press, pp. 71–90, 1975.Google Scholar
- G77.G.H. Glover and J.C. Sharp, “Reconstruction of ultrasound propagation speed distribution in soft tissue: time-of-flight tomography,” IEEE Trans. on Sonics and Ultrasonics, vol. SU-24, no. 4, July 1977.Google Scholar
- G78a.J.F. Greenleaf, S.K. Kenue, B. Rajagopalan, R.C. Bahn, and S.A. Johnson, “Breast imaging by ultrasonic computer-assisted tomography,” in Acoustical Imaging, vol. 8, A. Metherell, Ed. New York: Plenum Press, 1978.Google Scholar
- G78b.D.E. Gustafson, M.J. Berggren, M. Singh, and M.K. Dewanjee, “Computed transaxial imaging using single gamma emitters,” Radiology, vol. 129, pp. 187–194, Oct. 1978.Google Scholar
- H71.G.T. Herman and S. Rowland, “Resolution in ART: An experimental investigation of the resolving power of an algebraic picture reconstruction technique,” J. Theor. Biol., vol. 33, pp. 213–223, 1971.CrossRefGoogle Scholar
- H72.G.N. Hounsfield, “A method of and apparatus for examination of a body by radiation such as X ray or gamma radiation,” The Patent Office, London, Patent Specification 1283915, 1972.Google Scholar
- H73a.T. Hagfors and D.B. Campbell, “Mapping of planetary surfaces by radar,” Proc. IEEE, vol. 61, no. 9, pp. 1219–1225, September 1973.ADSCrossRefGoogle Scholar
- H73b.G.T. Herman and S.W. Rowland, “Three methods for reconstructing objects from X-rays: a comparative study,” Computer Graphics and Image Processing, vol. 2, pp. 151–178, 1973.CrossRefGoogle Scholar
- H73c.G.N. Hounsfield, “Computerized transverse axial scanning (tomography): Part 1. Description of system,” Br. J. Radiol., vol. 46, pp. 1016–1022, November 1973.CrossRefGoogle Scholar
- H75a.T.S. Huang, M. Kaveh and S. Berger, “Some further results in iterative image restoration,” presented at the Annual Meeting of the Optical Society of America, Boston, Mass., October 1975.Google Scholar
- H75b.H. Hurwitz, Jr., “Entropy Reduction in Bayesian analysis of measurements,” Phys. Rev., vol. 12, pp. 698–704, 1975.ADSCrossRefGoogle Scholar
- H76a.G.T. Herman, A.V. Lakshminarayanan, A. Naparstek, E.L. Ritman, R.A. Robb, and E.H. Wood, “Rapid computerized tomography,” Med. Data Process., pp. 582–598, 1976.Google Scholar
- H76b.E.J. Hoffman, M.E. Phelps, N.A. Mullani, C.S. Higgins, and M.M. TerPogossian, “Design and performance characteristics of a whole body transaxial tomography,” J. Nucl. Med., vol. 17, pp. 493–502, 1976.Google Scholar
- H76c.R.C. Hsieh and W.G. Wee, “On methods of three-dimensional reconstruction from a set of radioisotope scintigrams,” IEEE Trans. Syst. Man Cybern., vol. SMC-6, pp. 854–862, Dec. 1976.CrossRefGoogle Scholar
- H77a.G.T. Herman and A. Naparstek, “Fast image reconstruction based on a Radon inversion formula appropriate for rapidly collected data,” SIAM J. Appl. Math., vol. 33, pp. 511–533, Nov. 1977.MathSciNetMATHCrossRefGoogle Scholar
- H77b.B.P. Hildebrand and D.E. Hufferd, “Computerized reconstruction of ultrasonic velocity fields for mapping of residual stress,” in Acoustical Holography, Vol. 7, L.W. Kessler, Ed., New York: Plenum Press, pp. 245–262, 1977.Google Scholar
- H78a.P. Haque, D. Pisano, W. Cullen, and L. Meyer, “Initial performance evaluation of the CT 7000 scanner,” paper presented at the 20th Meeting of AAPM, San Francisco, CA, Aug. 1978.Google Scholar
- H78b.B.K.P. Horn, “Density reconstruction using arbitrary ray sampling scheme,” Proc. IEEE, vol. 66, pp. 551–562, May 1978.ADSCrossRefGoogle Scholar
- H79.B.P. Hildebrand and T.P. Harrington, “Maping residual stress by ultrasonic tomography,” Proc. Inst. Mech. E., pp. 105–116, May 1979.Google Scholar
- 170.K. Iwata and R. Nagata, “Calculation of three-dimensional refractive index distribution from interferograms,” J. Opt. Soc. of Am., vol. 60, pp. 133–135, 1970.CrossRefGoogle Scholar
- 175.K. Iwata and R. Nagata, “Calculation of refractive index distribution from interferograms using the Born and Rytov’s approximations,” Jap. J. Appl. Phys., vol. 14, pp. 1921–1927, 1975.CrossRefGoogle Scholar
- 178.R.D. Iverson, M.S. Thesis, Department of Electrical Engineering, University of Minnesota, 1978.Google Scholar
- J75a.S.A. Johnson, J.F. Greenleaf, A. Chu, J.D. Sjostrand, B.K. Gilbert and E.H. Wood, “Reconstruction of material characteristics from highly refraction distorted projections by ray tracing,” Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences. A Digest of Technical Papers, Stanford, California, pp. TRB2–1–TUB2–4, August 4-7, 1975.Google Scholar
- J75b.S.A. Johnson, J.F. Greenleaf, W.F. Samayoa, F.A. Duck and J.D. Sjostrand, “Reconstruction of three-dimensional velocity fields and other parameters by acoustic ray tracing,” 1975 Ultrasonic Symposium Proceedings, IEEE Cat. No. 75, pp. 46–51, CHP994-1SU, 1975.CrossRefGoogle Scholar
- J76.C.V. Jakowatz, Jr. and A.C. Kak, “Computerized tomography using X-rays and ultrasound,” School Elec. Eng., Purdue Univ., West Lafayette, IN, Res. Rep. TR-EE 76-25, 1976.Google Scholar
- J78a.P.M. Joseph and R.D. Spital, “A method for correcting bone induced artifacts in computed tomography scanners,” J. Compt. Assist. Tomog., vol. 2, pp. 100–108, Jan. 1978.CrossRefGoogle Scholar
- J78b.S.A. Johnson, J.F. Greenleaf, M. Tanaka, B. Rajagopalan, and R.C. Bahn, “Quantitative synthetic aperture reflection imaging with correction for refraction and attenuation: application of seismic techniques in medicine,” Proc. of the San Diego Biomedical Symposium, Vol. 17, Western Periodicals Co., North Hollywood, CA, pp. 337–349, 1978.Google Scholar
- J79.S.A. Johnson and J.F. Greenleaf, “New ultrasound and related imaging techniques,” IEEE Trans. on Nuclear Science, Vol. NS-26, No. 2, pp. 2812–2816, April 1979.ADSCrossRefGoogle Scholar
- K63.D.E. Kuhl and R.Q. Edwards, “Image separation radioisotope scanning,” Radiology, vol. 80, pp. 653–661, 1963.Google Scholar
- K77.A.C. Kak, C.V. Jakowatz, N.A. Baily, and R.A. Keller, “Computerized tomography using video recorded fluoroscopic images,” IEEE Trans. Biomed. Eng., vol. BME-24, pp. 157–169, Mar. 1977.CrossRefGoogle Scholar
- K78a.A.C. Kak and K.A. Dines, “Signal processing of broadband pulsed ultrasound: Measurement of attenuation of soft biological tissues,” IEEE Trans. Biomed. Eng., vol. BME-25, pp. 321–344, July 1978.CrossRefGoogle Scholar
- K78b.P.N. Keating, “More accurate interpolation using discrete Fourier transforms,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-26, pp. 368–369, 1978.CrossRefGoogle Scholar
- K78c.D.K. Kijewski and B.E. Bjarngard, “Correction for beam hardening in computed tomography,” Med. Phys., vol. 5, pp. 209–214, 1978.CrossRefGoogle Scholar
- K79a.A.C. Kak, “Image reconstruction from projections,” School Elec. Eng., Purdue Univ., West Lafayette, IN, Res. Rep. TR-EE-79-26, 1979.Google Scholar
- K79b.A.C. Kak, “Computerized tomography with X-ray emission and ultrasound sources,” PROC. IEEE, Vol. 67, No. 9, pp. 1245–1272, September 1979.CrossRefGoogle Scholar
- K79c.M. Kaveh, R.K. Mueller and R.D. Iverson, “Ultrasonic tomography based on perturbation solutions of the wave equation,” Computer Graphics and Image Processing, February 1979.Google Scholar
- K80.M. Kaveh, R.K. Mueller, R. Rylander, T.R. Coulter, and M Soumekh, “Experimental results in ultrasonic diffraction tomography,” this volume, pp. 433–50, 1980.Google Scholar
- L64.C. Lanczos, Linear Differential Operators, London: Van Nostrand, 1964.Google Scholar
- L75.A.V. Lakshminarayanan, “Reconstruction from divergent ray data,” Dep. Computer Science, State Univ. New York, Buffalo, Tech. Rep. 92, 1975.Google Scholar
- L80a.C.Q. Lee, “Tissue characterization by ultrasonic impediography,” this volume, pp. 521–532, 1980.Google Scholar
- L80b.S. Leeman, “Impediography Revisited,” this volume, pp. 513–320, 1980.Google Scholar
- M73.R.M. Mersereau, “Recovering multidimensional signals from their projections,” Computer Graphics and Image Processing, vol. 1, pp. 179–195, 1973.CrossRefGoogle Scholar
- M74a.E.C. McCullough, H.L. Baker, Jr., O.W. Houser, and D.F. Reese, “An evaluation of the quantitative and radiation features of a scanning X-ray transverse axial tomograph: The EMI scanner,” Radiation Phys. vol. 3, pp. 709–715, June 1974.Google Scholar
- M74b.R.M. Mersereau and A.V. Oppenheim, “Digital reconstruction of multidimensional Signals from Their Projections,” Proceedings of the IEEE, vol. 62, October 1974.Google Scholar
- M75a.E.C. McCullough, “Photon attenuation in computed tomography,” Med. Phys., vol. 2, pp. 307–320, 1975.CrossRefGoogle Scholar
- M75b.W.D. McDavid, R.G. Waggener, W.H. Payne, and M.J. Dennis, “Spectral effects on three-dimensional reconstruction from X-rays,” Med. Phys., vol. 2, pp. 321–324, 1975.CrossRefGoogle Scholar
- M77.J.G. Miller, M. O’Donnell, J.W. Mimbs, and B.E. Sobel, “Ultrasonic attenuation in normal and ischemic myocardium,” in Proc. 2nd Int. Symp. Ultrasonic Tissue Characterization (National Bureau of Standards), 1977.Google Scholar
- M78a.M. Millner, W.H. Payne, R.G. Waggener, W.D. McDavid, M.J. Dennis, and V.J. Sank, “Determination of effective energies in CT calibration,” Med. Phys., vol. 5, pp. 543–545, 1978.CrossRefGoogle Scholar
- M78b.N.A. Mullani, C.S. H’Iggins, J.T. Hood, and C.M. Curie, “PETT IV: Design analysis and performance characteristics,” IEEE Trans. Nucl. Sci., vol. NS-25, pp. 180–183, Feb. 1978.ADSCrossRefGoogle Scholar
- M79.R.K. Mueller, M. Kaveh and G. Wade, “Reconstructive tomography and applications to ultrasonics,” PROC. IEEE, Vol. 67, No. 4, pp. 567–587, April 1979.ADSCrossRefGoogle Scholar
- M80a.D. Mensa, G. Heidbreder, and G. Wade, “Aperture synthesis by object rotation in coherent imaging,” to be published in IEEE Transactions on Nuclear Science, April 1980.Google Scholar
- M80b.R.K. Mueller, M. Kaveh and R.D. Iverson, “A new approach to acoustic tomography using diffraction techniques,” in Acoustical Imaging, Vol. 8, Ed. A. Metherell, New York: Plenum Press, pp. 615–628, 1980.CrossRefGoogle Scholar
- M80c.R.K. Mueller and M. Kaveh, “Ultrasonic Diffraction Tomography,” Internal Report, Department of Electrical Engineering, University of Minnesota, 1980.Google Scholar
- N79.S.J. Norton and M. Linzer, “Ultrasonic reflectivity tomography: Reconstruction with circular transducer arrays,” Ultrasonic Imaging, vol. 1, no. 2, Apr. 1979.Google Scholar
- 061.W.H. Oldendorf, “Isolated flying spot detection of radiodensity discontinuities displaying the internal structural pattern of a complex object,” IRE Trans. Biomed. Elec., vol. BME-8, pp. 68–72, 1961.CrossRefGoogle Scholar
- P72.J.E.B. Ponsonby, I. Morison, A.R. Birks, and J.K. Landon, “Radar images of the moon at 75 and 185 cm wavelengths,” The Moon, vol. 5, pp. 286–294, Nov./Dec. 1972.ADSCrossRefGoogle Scholar
- P75.M.E. Phelps, E.J. Hoffman, and M.M. TerPogossian, “Attenuation coefficients of various body tissues, fluids and lesions at photon energies of 18 to 136 deV,” Radiology, vol. 117, pp. 574–583, 1975.Google Scholar
- P77a.T.M. Peters and R.M. Lewitt, “Computed tomography with fan-beam geometry,” J. Comput. Assist. Tomog., vol. 1, pp. 429–436, 1977.CrossRefGoogle Scholar
- P77b.M.E. Phelps, “Emission computed tomography,” Sem. Nucl. Med., vol. 7, pp. 334–365, Oct. 1977.CrossRefGoogle Scholar
- P78.M.E. Phelps, E.J. Hoffman, S.C. Huang, and D.E. Kuhl, “ECAT: A new computerized tomographic imaging system for positron-emitting radiopharmaceuticals,” J. Nucl. Med., vol. 19, pp. 635–647, 1978.Google Scholar
- R17.J. Radon, “Uber die bestimmung von funktionen durch ihre in-tergralwerte langs gewisser mannigfaltigkeiten,” (“On the determination of functions from their integrals along certain manifolds”), Berichte Saechsische Akademie der Wissenschaften, vol. 69, pp. 262–277, 1917.Google Scholar
- R69.P.D. Rowley, “Quantitative interpretation of three-dimensional weakly refractive phase objects using holographic interferometry,” J. Opt. Soc. Am., vol. 59, pp. 1496–1498, November 1969.CrossRefGoogle Scholar
- R71a.G.N. Ramachandran and A.V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: II. Application of convolutions instead of Fourier transforms,” Proc. Nat. Acad. Sci., vol. 68, no. 9, pp. 2236–2240, 1971.MathSciNetADSCrossRefGoogle Scholar
- R71b.G.N. Ramachandran and A.V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: III. Description and application of the convolution method,” Indian J. Pure Appl. Phys., vol. 9, pp. 997–1003, 1971.Google Scholar
- R76.S.W. Rowland, “The effect of noise in the projection data on the reconstruction produced by computerized tomography,” Proc. soc. Photo-Opt. Instrum. Eng., vol. 96, pp. 124–130, 1976.Google Scholar
- R78.S.J. Riederer, N.J. Pelc, and D.A. Chesler, “The noise power spectrum in computer X-ray tomography,” Phys. Med. Biol., vol. 23, pp. 446–454, 1978.CrossRefGoogle Scholar
- 567.D. Slepian, “Linear least squares filtering of distorted images,” J. of Opt. Soc. of America, vol. 57, pp. 918–922, July 1967.ADSCrossRefGoogle Scholar
- 568.J.W. Strohbehn, “Line of sight wave propagation through turbulent atmosphere,” IEEE Proceedings, vol. 56, pp. 1301–1318, August 1968.CrossRefGoogle Scholar
- S73.D.W. Sweeney and G.M. Vest, “Reconstruction of three-dimensional refractive index fields from multidimensional interferometric data,” Applied Optics, vol. 2, 1973.Google Scholar
- S77a.L.A. Shepp and J.A. Stein, “Simulated reconstruction artifacts in computerized X-ray tomography,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M.M. TerPogossian et al., Eds. Baltimore, MD: University Park Press, 1977.Google Scholar
- S77b.R.A. Shulz, E.C. Olson, and K.S. Han, “A comparison of the number of rays vs. the number of views in reconstruction tomography,” Proc. Soc. Photo-Opt. Instrum. Eng., vol. 127, pp. 313–320, 1977.Google Scholar
- 578.H.J. Scudder, “Introduction to computer aided tomography,” Proc. IEEE Trans. Nucl. Sci., vol. NS-21, pp. 21–43, 1974.Google Scholar
- 579.F. Stanger and S.A. Johnson, “Ultrasonic transmission tomography based on the inversion of the Helmholtz wave equation for plane and spherical wave insonification,” Applied Mathematics Notes, Canadian Mathematical Soc, Ottawa, Ontario, Canada, Vol. 4, No. 3-4, pp. 102–127, December 1979.Google Scholar
- T61.V.I. Tatarski, Wave Propagation in a Turbulent Medium, New York: McGraw-Hill, 1961.MATHGoogle Scholar
- T65.J.H. Thomson, Talk presented at the Symposium on Planetary Atmospheres and Surfaces, Dorado, Puerto Rico, 1965.Google Scholar
- T67.M.M. TerPogossian, The Physical Aspects of Diagnostic Radiology. New York: Harper and Row, 1967.Google Scholar
- T68.J.H. Thomson and J.E.B. Ponsonby, “Two-dimensional aperture synthesis in lunar radar astronomy,” Proc. Roy. Soc. A., vol. 303, pp. 477–491, March 1968.ADSCrossRefGoogle Scholar
- T69.O. Tretiak, M. Eden, and M. Simon, “Internal structures for three dimensional images,” in Proc. 8th Int. Conf. Med. Biol. Eng. (Chicago, IL), 1969.Google Scholar
- T73.O. Tretiak, “Recovery of multi-dimensional signals from their projections,” Computer Graphics and Image Processing, vol. 1, pp. 179–195, October 1973.Google Scholar
- T75.E. Tanaka and Y.A. Iinuma, “Correction functions for optimizing the reconstructed image in transverse section scan,” Phys. Med. Biol., vol. 20, p. 789, 1975.CrossRefGoogle Scholar
- T77.M.M. TerPogossian, “Basic principles of computer axial tomography,” Sem. Nucl. Med., vol. VII, pp. 109–127, Apr. 1977.CrossRefGoogle Scholar
- T78a.K.C. Tam, G. Chu, V. Perez-Mendez, and C.B. Lin, “Three dimensional reconstruction in planar positron cameras using Fourier deconvolution of generalized tomograms,” IEEE Trans. Nucl. Sci., vol. NS-25, pp. 152–159, Feb. 1978.ADSCrossRefGoogle Scholar
- T78b.M.M. TerPogossian, N.A. Mullani, J. Hood, C.S. Higgins, and C.M. Curie, “A multistate positron emission computed tomography (PETT-IV) yielding transverse and longitudinal images,” Radiology, vol. 128, pp. 477–484, Aug. 1978.Google Scholar
- T78c.M.M. TerPogossian, N.A. Mullani, and J.J. Hood, C.S. Higgins, and D.C Ficke, “Design cnsideration for a positron emission transverse tomography (PETT-IV) for the imaging of the brain,” J. Comput. Assist. Tomog., vol. 2, pp. 439–444, Nov. 1978.CrossRefGoogle Scholar
- T78d.O.J. Tretiak, “Noise limitations in X-ray computed tomography,” J. Comput. Assist. Tomog., vol. 2, pp. 477–480, Sept. 1978.CrossRefGoogle Scholar
- W51.F.R. Wrenn, Jr. M.L. Good, and P. Handler, “The use of positron-emitting radioisotope for the localization of brain tumors,” Nature, vol. 113, pp. 525–527, 1951.Google Scholar
- W69.E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Optics Communications, vol. 1, pp. 153–156, 1969.ADSCrossRefGoogle Scholar
- W76.G. Wade, “Historical perspectives,” in Acoustic Imaging, Ed. G. Wade, New York: lenum Press, pp. 21–42, 1976.Google Scholar
- W77a.P.N.T. Wells, “Ultrasonics in medicine and biology,” Phys. Med. Biol., vol. 22, pp. 629–669, 1977.CrossRefGoogle Scholar
- W77b.L. Wang, “Cross-section reconstruction with a fan-beam scanning geometry,” IEEE Trans. Comput., vol. C-26, pp. 264–268, Mar. 1977.CrossRefGoogle Scholar
- W78a.G. Wade, R.K. Mueller, and M. Kaveh, “A survey of techniques for ultrasonic tomography,” in Proceedings of IFIP TC-4 Working Conference on Computer-Aided Tomography and Ultrasonics in Medicine, Ed. J. Raviv, Amsterdam: North-Holland, pp. 165–215, 1978.Google Scholar
- W78b.G.H. Williams, “The design of a rotational X-ray CT scanner,” Medita, (Proc. MEDEX 78), vols. 6 and 7, pp. 47–53, June 1978.Google Scholar
- W80a.G. Wade, S. Elliott, I. Khogeer, G. Flesher, J. Eisler, D. Mensa, N.S. Ramesh, and G. Heidbreder, “Acoustic echo computer tomography,” in Acoustic Holography, vol. 8, Ed. A. Metherell, New York: Plenum Press, pp. 565–576, 1980.Google Scholar
- W80b.G. Wade and D. Mensa, “Pulse echo and Doppler reconstructive tomography,” to be published in Proceedings of the 1980 International Optical Computing Conference, 1980.Google Scholar
- Y77.M. Yaffe, A. Fenster, and H.E. Johns, “Xenon ionization detectors for fan-beam computed tomography scanners,” J, Comput. Assist. Tomog., vol. 1, pp. 419–428, 1977.CrossRefGoogle Scholar
- Y77.Y. Yamamoto, C.J. Thompson, E. Meyer, J.S. Robertson, and W. Feindel, “Dynamic positron emission tomography for study of cerebral hemodynamics in a cross-section of the head using positron-emitting 68Ga-EDTA and 77Kr,” J. Comput. Assist. Tomog., vol. 1, pp. 43–56, Jan. 1977.CrossRefGoogle Scholar
- Z35.F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen beobacktung,” (“The phase contrast method of microscopic observation”), Z. Tech. Phys., vol. 16, pp. 454, 1935.Google Scholar