Diffraction Tomography: It's Application in Ultrasound

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Omer M. Gaddoura 1 Mingyue Ding 1

1. School of Life Science and Technology, Huazhong University of Science and Technology, Wuhan, China

* Corresponding author.

DOI: https://doi.org/10.5815/ijem.2011.04.02

Received: 26 Mar. 2011 / Revised: 16 Jun. 2011 / Accepted: 22 Jul. 2011 / Published: 29 Aug. 2011

Index Terms

Ultrasound, Diffraction Tomography, Interpolation, B-spline


Ultrasound Diffraction Tomography (UDT) is an important alternative to conventional B-mode imaging. Generally, in diffraction tomography, the most universal available computational strategies for reconstructing the object from its projections are interpolation in the frequency domain and interpolation in the space domain. They are analogous to the direct Fourier inversion and backprojection algorithms of straight ray tomography. In this paper two B-spline interpolation functions are introduced. Due to the computational expenses in the space domain interpolation, we apply the interpolation in the frequency domain to implement our new interpolation functions. We also compare our results with filtered backprojection algorithm result. The validity and feasibility of our method was tested using an agar phantom to mimic the human tissue, olive to mimic the cancer, and water to mimic the cyst. The experimental results show that this method has a promising impact in clinical applications.

Cite This Paper

Omer M. Gaddoura,Mingyue Ding,"Diffraction Tomography: It's Application in Ultrasound", IJEM, vol.1, no.4, pp.10-17, 2011. DOI: 10.5815/ijem.2011.04.02 


[1]M. Fatemi and A. C. Kak, “Ultrasonic B-scan Imaging: Theory of Image Formation and a Technique for Restoration”. Ultrasonic Imaging. 2, 1– 48, 1980.

[2]A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. Philadelphia. PA: SIAM, 2001.

[3]X. Pan, Unified Reconstruction Theory for Diffraction Tomography, with Consideration of noise Control. J. Opt. Soc. Amer. 15, 2312–2326, 1998.

[4]X. Pan, Consistency Conditions and Linear Reconstruction Methods in Diffraction Tomography. IEEE Trans. Med. Imag. 19, 51–54, 2000.

[5]A. Devaney, A Filtered Backpropagation Algorithm for Diffraction Images. Ultrason. Imag. 4, 336–350, 1982.

[6]R. K. Mueller, M. Kaveh, and G. Wade, Reconstructive Tomography and Applications to Ultrasonics. Proc. IEEE. 67, 567–587, 1979. 

[7]J. F. Greenleaf, S. A. Johnson, S. L. Lee, G. T. Herman, and E. H. Wood, Algebraic Reconstruction of Spatial Distributions of Acoustic Absorption with Tissues from Their Two-Dimensional Acoustic Projections. Acoustical Holography. 5, 591–603, 1974.

[8]J. F. Greenleaf, S. A. Johnson, W. F. Samayoa, and F. A. Duck, Algebraic Reconstruction of Spatial Distributions of Acoustic Velocities in Tissue from Their Time-of-Flight Profiles. Acoustical Holography. 6, 71–90, 1975. 

[9]J. F. Greenleaf, S. A. Johnson, and A. H. Lent, Measurement of Spatial Distribution of Refractive Index in Tissues by Ultrasonic Computer Assisted Tomography. Ultrasound Med. Biol. 3, 327–339, 1978.

[10]J. F. Greenleaf and R. C. Bahn, Clinical Imaging with Transmissive Ultrasonic Computerized Tomography. IEEE Trans. Biomed. Eng. BME-28, 177–185, 1981.

[11]A. C. Kak, Computerized Tomography with X-ray Emission and Ultrasound Sources. Proc. IEEE. 67, 1245–1272, 1979.

[12]F. Stenger and S. A. Johnson, Ultrasonic Transmission Tomography Based on the Inversion of the Helmholtz Equation for Plane and Spherical Wave Insonification. Appl. Math. Notes. 4, 102–127, 1979.

[13]K. Iwata and R. Nagata, Calculation of Refractive Index Distribution from Interferograms using Born and Rytov’s approximation. Japan J. Appl. Phys. 14, 1975.

[14]R. K. Mueller, M. Kaveh, and R. D. Inverson, A New Approach to Acoustic Tomography Using Diffraction Techniques. Acoustical Imaging. 8, 615–628, 1980.

[15]M. Kaveh, R. K. Mueller, and J. F. Greenleaf, Fourier Domain Reconstruction Methods with Application to Diffraction Tomography. Acoustical Imaging. 13, 17–30, 1984.

[16]S. X. Pan and Avinash C. KAK, A Computational Study of Reconstruction Algorithms for Diffraction Tomography: Interpolation Versus Filtered Backpropagation. IEEE Transaction On Acoustic, Speech, and Signal Processing. Vol ASSP.31, No.5, 1983.

[17]A. Ishimaru.: Wave Propagation and Scattering in Random Media. New York: Academic. 2, (1978)

[18]L. A. Shepp and B. F. Logan.: The Fourier Reconstruction of a Head Section. IEEE Trans. Nucl. Sci. NS-21, 21{43 (1974)