Abstract
The problem of reconstructing a binary image (usually an image in the plane and not necessarily on a Cartesian grid) from a few projections translates into the problem of solving a system of equations which is very underdetermined and leads in general to a large class of solutions. It is desirable to limit the class of possible solutions, by using appropriate prior information, to only those which are reasonably typical of the class of images which contains the unknown image that we wish to reconstruct. One may indeed pose the following hypothesis: if the image is a typical member of a class of images having a certain distribution, then by using this information we can limit the class of possible solutions to only those which are close to the given unknown image. This hypothesis is experimentally validated for the specific case of a class of binary images representing cardiac cross-sections, where the probability of the occurrence of a particular image of the class is determined by a Gibbs distribution and reconstruction is to be done from the three noisy projections.
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References
Herman, G.T., Kuba, A. (eds.): Special Issue on Discrete Tomography. Int. J Imaging Syst. and Technol. 9 No. 2/3 (1998)
Chang, S.-K., Chow, C. K.: The Reconstruction of Three-Dimensional Objects from Two Orthogonal Projections and its Application to Cardiac Cineangiography. IEEE Trans. on Computers 22 (1973) 18–28
Fishburn, P., Schwander, P., Shepp, L., Vanderbei, R.J.: The Discrete Radon Transform and its Approximate Inversion via Linear Programming. Discrete Applied Mathematics 75 (1997) 39–61
Chan, M.T., Herman, G.T., Levitan, E.: A Bayesian Approach to PET Reconstruction Using Image-Modeling Gibbs Priors: Implementation and Comparison. IEEE Trans. Nucl. Sci. 44 (1997) 1347–1354
Winkler, G.: Image Analysis, Random Fields and Dynamic Monte Carlo Methods. Springer-Verlag, Berlin Heidelberg New York (1995)
Levitan, E., Chan, M., Herman, G.T.: Image-Modeling Gibbs Priors. Graph. Models Image Proc. 57 (1995) 117–130
Matej, S., Vardi, A., Herman, G.T., Vardi, E.: Binary Tomography Using Gibbs Priors. In Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhauser, Boston Cambridge (to appear)
Ryser, H.J.: Combinatorial Properties of Matrices of Zeros and Ones. Can. J. Mathematics 9 (1957) 371–377
Kong, T.Y., Herman, G.T.: Tomographic Equivalence and Switching Operations. In Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhauser, Boston Cambridge (to appear)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of State Calculations by Fast Computing Machines. J. Chem. Phys. 21, (1953) 1087–1092
Ritman, E.L., Robb, R.A., Harris, L.D.: Imaging Physiological Functions. Praeger, New York (1985)
Browne, J.A., Herman, G.T., Odhner, D.: SNARK93: A Programming System for Image Reconstruction from Projections. Technical Report No. 198. Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia (1993)
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Carvalho, B.M., Herman, G.T., Matej, S., Salzberg, C., Vardi, E. (1999). Binary Tomography for Triplane Cardiography. In: Kuba, A., Šáamal, M., Todd-Pokropek, A. (eds) Information Processing in Medical Imaging. IPMI 1999. Lecture Notes in Computer Science, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48714-X_3
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DOI: https://doi.org/10.1007/3-540-48714-X_3
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