Abstract
An analytical (noniterative) approach to nonuniformly attenuated brain SPECT without transmission scans has been developed. This approach treats the Poisson noise of projection data by a Wiener filter after a square-root transformation. It removes scatter portion in primary-energy-window measurements by subtracting a fraction of smoothed secondary-energy-window samples. Resolution variation as a function of depth from the collimator is corrected by a depth-dependent deconvolution using the variation kernel. The approach enlarges the head boundary radially for a uniform attenuation map to overcome the nonuniform attenuation of the skull and scalp. Attenuation by the head is then compensated in inverting the uniformly attenuated Radon transform. Studies using patient head CT (for the attenuation map), point-source measurement (for the resolution kernel), and the Hoffman brain phantom demonstrated accurate reconstruction by the enlarged uniform attenuation map (< 1% ROI error), as compared to the reconstruction using the true head attenuation map.
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References
Anscombe, F.J. (1948) The Transformation of Poisson, Binomial and Negative-Binomial Data. Biometrika 35, 246–254.
Appledorn, A.R. (1989) An Analytical Solution to the Nonstationary Reconstruction Problem in SPECT. Proc IPMI 11, 69–79.
Bellini, A., Piacentini, M., Cafforio, C., and Rocca, F. (1979) Compensation of Tissue Absorption in Emission Tomography. IEEE Trans ASSP 27, 213–218.
Chang, C.T. (1978) A Method for Attenuation Correction in Radionuclide CT. IEEE Trans Nucl Sci 25, 638–643.
Clough, A.V. and Barrett, H.H. (1983) Attenuated Radon and Abel Transforms. J Opt Soc Am 73, 1590–1595.
Edholm, P.R., Lewitt, R.M., and Lindholm, B. (1986) Novel Properties of the Fourier Decomposition of the Sinogram. Proc SPIE 671, 8–18.
Formiconi, A., Passeri, A., Pupi, A., and Comis, G. (1990) High Resolution Brain SPECT with Accurate Modeling of Spatial System Response, Attenuation and Scatter. J Nucl Med 31, 739P.
Furuie, S.S. and Mascarenhas, N.D.A. (1992) Tomographic Reconstruction of Images with Poisson Noise: Projection estimation. Automedica 15, 133–140.
Glick, S.J., Penney, B.C., King, M.A., and Byrne, C.L. (1994a) Noniterative Compensation for the Distance-Dependent Detector Response and Photon Attenuation in SPECT Imaging. IEEE Trans Med Imag 13, 363–374.
Glick, S.J., King, M.A., and Pan, T.S., and Licho, R. (1994b) Compensation for Nonuniform Attenuation in SPECT Brain Imaging. J Nucl Med 35, 188P.
Goodman, J.W. and Belsher, J.F. (1976) Fundamental Limitations in Linear Invariant Restoration of Atmospherically Degraded Images. Proc SPIE 75, 141–154.
Gullberg, G.T. (1979) The Attenuated Radon Transform: Theory and application in medicine and biology. Ph.D. Thesis, Donner Laboratory, University of California, CA.
Gullberg, G.T. and Budinger, T.F. (1981) The Use of Filtering Methods to Compensate for Constant Attenuation in SPECT. IEEE Trans BME 28, 142–157.
Hawkins, W.G., Leichner, P.K., and Yang, N.C. (1988) The Circular Harmonic Transform for SPECT Reconstruction and Boundary Conditions on the FT of the Sinogram. IEEE Trans Med Imag 7, 135–148.
Hoffman, E., Cutler, P., Digby, W., and Mazziotta, J. (1990) 3D Phantom to Simulate Cerebral Blood Flow and Metabolic Images for PET. IEEE Trans Nucl Sci 37, 616–620.
Hoshi, H., Ohnishi, T., Jinnouchi, S., Futami, S., Nagamachi, S., Kodama, T., Watanabe, K., Ueda, T., and Wakisaka, S. (1994) Cerebral Blood Flow Study in Patients with Moyamoya Disease Evaluated by IMP SPECT. J Nucl Med 35, 44–50.
Huesman, R.H., Gullberg, G.T., Greenberg, W.L., and Budinger, T.F. (1977) Donner Algorithms for Reconstruction Tomography. Lawrence Berkeley Laboratory, University of California, CA.
Inouye, T., Kose, K., and Hasegawa, A. (1989) Image Reconstruction Algorithm for SPECT with Uniform Attenuation. Phys Med Biol 34, 299–304.
Jaszczak, R.J., Greer, K.L., Floyd, C.E., Harris, C.C., and Coleman, R.E. (1984) Improved SPECT Quantification Using Compensation for Scattered Photons. J Nucl Med 25, 893–900.
Kim, K.I., Tewarson, R.P., Bizais, Y., and Rowe, R.W. (1984) Inversion for the Attenuated Radon Transform with Constant Attenuation. IEEE Trans Nucl Sci 31, 538–542.
King, M.A., Hademenos, G.S., and Glick, S.J. (1992) A Dual Photo-Peak Window Method for Scatter Correction. J Nucl Med 33, 605–612.
Lewitt, R.M., Edholm, P.R., and Xia, W. (1989) Fourier Method for Correction of Depth-Dependent Collimator Blurring. Proc SPIE Med Imag III 1092, 232–243.
Liang, Z., Jaszczak, R.J., Floyd, C.E., Greer, K.L., and Coleman, R.E. (1988) Bayesian Reconstruction of SPECT in Parallel, Fan, and Cone Beam Geometries. J Nucl Med 29, 871P.
Liang, Z., Jaszczak, R.J., Floyd, C.E., Greer, K.L., and Coleman, R.E. (1989) Reprojection and Backprojection in SPECT Image Reconstruction. Proc IEEE Southeast 1, 919–926.
Liang, Z., Turkington, T.G., Gilland, D.R., Jaszczak, R.J., and Coleman, R.E. (1992) Simultaneous Compensation for Attenuation, Scatter, and Detector Response for SPECT Reconstruction in Three Dimensions. Phys Med Biol 37, 587–603.
Liang, Z., Ye, J., and Harrington, D.P. (1994) An Analytical Approach to Quantitative Reconstruction of Non-Uniform Attenuated Brain SPECT. Phys Med Biol 39, 2023–2041.
Liang, Z., Ye, J., Cheng, J., and Harrington, D.P. (1995) On the Inversion of the Exponential Radon Transform for Quantitative Brain SPECT Submitted to Phys Med Biol.
Markoe, A. (1984) Fourier Inversion of the Attenuated X-Ray Transform. SIAM J Math Anal 15, 718–722.
Natterer, F. (1979) On the Inversion of the Attenuated Radon Transform. Numer Math 32, 431–438.
Ogawa, K., Harata, Y., Ichihara, T., Kubo, A., and Hashimoto, S. (1991) A Practical Method for PositionDependent Compton-Scatter Correction in SPECT. IEEE Trans Med Imag 10, 408–412.
Ohnishi, T., Hoshi, H., Nagamachi, S., Jinnouchi, S., Flores, L.G., Futami, S., Watanabe, K. (1995) High Resolution SPECT to Assess Hippocampal Perfusion in Neurospychiatric Diseases. J Nucl Med 36, 1163–1169.
Palestro, C.J., Sen, C., Muzinic, M., Afriyie, M., and Goldsmith, S.J. (1993) Assessing Collateral Cerebral Perfusion with Technetium-99m-HMPAO SPECT During Temporary Internal Carotid Artery Occlusion. J Nucl Med 34, 1235–1238.
Soares, E.J., Byrne, C.L., Glick, S.J., Appledorn, C.R., and King, M.A. (1993) Implementation and Evaluation of an Analytical Solution to the Photon Attenuation and Nonstationary Resolution Reconstruction Problem in SPECT. IEEE Trans Nucl Sci 40, 1231–1237.
Takana, E., Toyama, H., and Murayama, H. (1984) Convolutional Image Reconstruction for Quantitative SPECT. Phys Med Biol 29, 1489–1500.
Tomitani, T. (1986) A Deconvolution Function for SPECT with Constant Attenuation. IEEE Trans Nucl Sci 33, 505–510.
Tretiak, O.J. and Metz, C.E. (1980) The Exponential Radon Transform. SIAM J Appl Math 39, 341–354.
Van Elmbt, L. and Walrand, S. (1993) Simultaneous Correction of Attenuation and Distance-Dependent Resolution in SPECT: An analytical approach. Phys Med biol 38, 1207–1217.
Walters, T.E., Simon, W., Chesler, D.A., and Correia, J.A. (1981) Attenuation Correction in Gamma ECT. J Comput Assist Tomog 5, 89–94.
Xia, W., Lewitt, R.M., and Edholm, P.R. (1993) Fourier Correction for Spatially Variant Collimator Blurring in SPECT. IEEE Trans Med Imag 14, 100–115.
Ye, J, Liang, Z., and Harrington, D.P. (1994) Quantitative Reconstruction for Myocardial Perfusion SPECT: An efficient approach by depth-dependent deconvolution and matrix rotation. Phys Med Biol 39, 1263–1279.
Ye, J., Liang, Z., and Harrington, D.P. (1995) Accurate Analytical Compensation for Nonuniformly Attenuated Brain SPECT Using Enlarged Uniform Map. Conf Record IEEE NSS —MIC 33, 4M09.
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Liang, Z., Ye, J., Cheng, J., Harrington, D.P. (1996). Quantitative Brain SPECT in three Dimensions. In: Grangeat, P., Amans, JL. (eds) Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine. Computational Imaging and Vision, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8749-5_9
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DOI: https://doi.org/10.1007/978-94-015-8749-5_9
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