A Statistical Estimation Approach to Medical Image Reconstruction from Ultrasonic Array Data

  • E. J. Pisa
  • C. W. Barnes
Part of the Acoustical Imaging book series (ACIM, volume 10)


Images that purport to represent the distribution of scattering objects in living tissue can be generated from ultrasonic pulse-echo data by a number of means. In the simplest form, pulses are transmitted and received on a single fixed-focus transducer that is scanned mechanically or by hand to generate a conventional B-scan image.


Minimum Mean Square Error Point Scatterer Kalman Gain Minimum Mean Square Error Estimate Minimum Mean Square Error Estimator 


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  1. 1.
    Hubelbank, M., and 0. Tretiak. Tretiak. “Focused Ultrasonic Transducer Design,” M.I.T. Electronics Res. Lab Report No. 98, 1970, 169–177.Google Scholar
  2. 2.
    Walker, J. T., and J. D. Meindl. “A Digitally Controlled CCD Dynamically Focused Phased Array,” Proc. IEEE Ultrasonics Symposium, 1975, 80–83.Google Scholar
  3. 3.
    Norton, S. J. “Theory of Acoustic Imaging,” Ph.D. Thesis, Stanford University, Stanford Electronic Lab. Tech Report No. 4956–2, 1976.Google Scholar
  4. 4.
    McKeighen, R. E., and M. P. Buchin. “New Techniques for Dynamically Variable Electronic Delays for Real Time Ultrasonic Imaging,” Proc. IEEE Ultrasonics Symposium, 1977, 250–254.Google Scholar
  5. 5.
    Corl, P. D., and G. S. Kino. “A Real-Time Synthetic Aperture Imaging System,” in Acoustical Imaging, Vol. 9, K. Wang editor. New York: Plenum Press, 1980, 341–355.CrossRefGoogle Scholar
  6. 6.
    Norton, S. J., and M. Linzer. “Ultrasonic Reflectivity Tomography: Reconstruction with Circular Transducer Arrays,” Ultrasonic Imaging, 1, 1979, 154–184.CrossRefGoogle Scholar
  7. 7.
    Norton, S. J. “Reconstruction of a Reflectivity Field from Line Integrals Over Circular Paths,” J. Acoust. Soc. Am., 67 (3), March 1980, 853–863.MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Norton, S. J. “Reconstruction of a Two-Dimensional Reflecting Medium Over a Circular Domain: Exact Solution,” J. Acoust. Soc. Am., 67 (4), April 1980, 1266–1273.MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Morse, P. M., and K. U. Ingard. Theoretical Acoustics. New York: McGraw-Hill, 1968.Google Scholar
  10. 10.
    Duckworth, G. L. “Adaptive Array Processing for Acoustic Imaging,” in Acoustical Imaging, Vol. 9, K. Wang editor. New York: Plenum Press, 1980, 177–201.CrossRefGoogle Scholar
  11. 11.
    Luenberger, D. G. Optimization by Vector Space Methods. New York: Wiley, 1969.MATHGoogle Scholar
  12. 12.
    Schweppe, F. C. Uncertain Dynamic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1973.Google Scholar
  13. 13.
    Atkinson, K. E. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. Philadelphia, PA: SIAM, 1976.Google Scholar
  14. 14.
    Meditch, J. S. Stochastic Optimal Linear Estimation and Control. New York: McGraw-Hill, 1969.MATHGoogle Scholar
  15. 15.
    Anderson, B.D.O., and J. B. Moore. Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.MATHGoogle Scholar
  16. 16.
    Wood, S. L., A. Macovski, and M. Morf. “Reconstructions with Limited Data Using Estimation Theory,” in Computer Aided Tomography and Ultrasonics in Medicine, Raviv. editors, IFIP, North Holland Pub. Co., 1979, 219–233.Google Scholar
  17. 17.
    Mason, W. P. Electromechanical Transducrs and Wave Filters. Princeton, NJ: Van Nostrand, 1948.Google Scholar
  18. 18.
    Auld, B. A. Acoustic Fields and Waves in Solids, Vol. 1, Ch. 8. New York: Wiley, 1973Google Scholar
  19. 19.
    Sachse, W., and N. N. Hsu. “Ultrasonic Transducers for Materials Testing and Their Characterization,” in Physical Acoustics, XIV, Mason and Thurston editors. New York: Academic Press, 1979.Google Scholar
  20. 20.
    Stepanishen, P. R. “Transient Radiation from Pistons in a Finite Planar Baffle,” J. Acoust. Soc. Am., 49, 5 (part 2 ), 1971, 1629–1638.CrossRefGoogle Scholar
  21. 21.
    Stepanishen, P. R. “The Time-Dependent Force and Radiation Impedance on a Piston in a Rigid Infinite Planar Baffle,” J. Acoust. Soc. Am., 49, 3(Part 2 ), 1971, 841–849.ADSCrossRefGoogle Scholar
  22. 22.
    Barnes C. W. Mathematical Modeling of Ultrasonic Array Imaging Systems, Tech. Rpt. 79–1, Rohe Scientific Corp., Santa Ana, CA., March 1979.Google Scholar
  23. 23.
    Lockwood, J. C., and J. G. Willette. “High-Speed Method for Computing the Exact Solution for the Pressure Variations in the Nearfield of a Baffled Piston,” J. Acoust. Soc. Am., 53, 3, 1973, 735–741; Erratum: 54, 6, 1973, p. 1762.Google Scholar
  24. 24.
    O’DoniiTl, M., E. T. Jaynes, and J. G. Miller. “Mechanisms: Relationship Between Ultrasonic Attenuation and Dispersion,” Third Int. Symp. Ultrasonic Imaging and Tissue Characterization, June 5–7, 1978; N.B.S., Gaithersburg, MD, p. 36 of program and abstracts.Google Scholar

Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • E. J. Pisa
    • 1
  • C. W. Barnes
    • 2
  1. 1.Rohe Scientific Corp.Philips Medical SystemsSanta AnaUSA
  2. 2.School of EngineeringUniversity of California, IrvineIrvineUSA

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