Abstract
Theorems and a transformation formula are developed for the 2D exponential Radon transform (ERT) whereby theorems for the number of nodes of radial modulators of the X-ray transform (no attenuation of internal sources) can be extended to the ERT. The results were applied to SPECT simulations with angular under-sampling, and a spectral filter was shown to improve image quality in the region affected by angular aliasing, without altering interior regions that were not affected by angular aliasing.
Keywords
- Single Photon Emission Compute Tomography
- Transformation Formula
- Line Integral
- Radial Modulator
- Spectral Filter
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References
Cormack, A.M., "Representations of a Function by its Line Integrals, with some Applications," J. Appl. Phys. 344(9), Sep. 1963. pp. 2722–2727.
Cormack, A.M., "Representations of a Function by its Line Integrals, with Some Applications,", J. Appl Phys. 35(10), Oct. 1964, pp 2908–2913.
Hawkins, W.G., Dissertation, Dept. of Appl. Math., Univ. of Arizona, Tucson, Az., 1982.
Hawkins, W.G., PK Leichner & N-C Yang, "The Circular Harmonic Transform for SPECT and Boundary Conditions on the Fourier Transform of the Sinogram," IEEE Trans. MI 7(2), Jun 1988, pp 135–148.
Knesaurek, K, King, MA, Glick, SJ & Penney, BC, "A 3-D non-stationary simulation of SPECT imaging," J. Nucl. Med., 30, pp 1666–1675, May, 1989.
Penney, BC, King, MA & Knesaurek, K, "A projector, backprojector pair which accounts for the two dimensional depth and distance dependent blurring in SPECT," IEEE Trans NS, in press.
Jaszczak RJ, Coleman RE, Lim CB, "SPECT: Single Photon Emission Computed Tomography," IEEE NS, 27(3), June 1980, pp 1137–1153.
Snyder DL, Cox RJ, "An Overview of Reconstructive Tomography and Limitations Imposed by a Finite Number of Projections," in: Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, MM Ter-Pogosian et. al. eds., University Park Press, Baltimore, MD, 1977, pp 3–32.
Huesman RH, “The effects of a Finite Number of Projection Angles and Finite Lateral Sampling on the Propagation of Statistical Errors in Transverse Section Reconstruction," Phys. Med. Biol., 22(4), 1985, pp 409–415.
Edholm PR, Lewitt RW, Lindholm B, "Novel Properties of the Fourier Transform of the Sinogram," SPIE Proc. 671, Apr 1986, pp 8–18.
Hawkins WG, Leichner PK, Yang N-C, "Validation of the Circular Harmonic Transform for Quantitative SPECT," to appear in J. Nucl. Med.
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© 1991 Springer-Verlag Berlin Heidelberg
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Hawkins, W.G., Yang, NC., Leichner, P.K. (1991). Theorems for the number of zeros of the projection radial modulators of the 2D exponential radon transform. In: Herman, G.T., Louis, A.K., Natterer, F. (eds) Mathematical Methods in Tomography. Lecture Notes in Mathematics, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084519
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DOI: https://doi.org/10.1007/BFb0084519
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