Abstract
This paper describes an algebraic algorithm for volume reconstruction from cone-beam projections. Since this is an ill-posed problem, regularization is necessary. While standard regularization methods are based on a smoothness assumption, we propose a regularizing process which preserves the reconstructed object edges. This method involves the minimization of a non quadratic energy criterion, difficult to solve, which we transform into a half-quadratic dual energy system, simple to minimize. Moreover, we have used two approaches to reduce the reconstruction time: storage of the non-null elements of the projection matrix and restriction of the reconstruction to the region of support. This method is developed for thyroid pinhole emission imaging. We present some results on a thyroid simulation and on a thyroid phantom using single circular orbit acquisition geometry. This method runs on conventional workstations within acceptable times. This regularized algebraic method gives high quality results and can be used in clinical practice.
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References
Aubert, G., Blanc-Féraud, L., Barlaud, M., and Charbonnier, P. (1994). A Deterministic Algorithm for Edge-Preserving Computed Imaging Using Legendre Transform. Proceedings of the 12 th International Conference on Pattern Recognition (Jerusalem, Israël), pages 188–191.
Blanc-Féraud, L., Charbonnier, P., Aubert, G., and Barlaud, M. (1995). Nonlinear Image Processing: Modeling and Fast Algorithm for Regularization with Edge Detection. Proceedings of the second IEEE ICIP (Washington, D.C., USA), 1:474–477.
Charbonnier, P., Aubert, G., Blanc-Féraud, L., and Barlaud, M. (1994a). Two Deterministic Half-Quadratic Regularization Algorithms for Computed Imaging. Proceedings of the first IEEE ICIP (Austin, USA).
Charbonnier, P., Blanc-Féraud, L., Aubert, G., and Barlaud, M. (1994b). Deterministic Edge-Preserving Regularization in Computed Imaging. Submitted to IEEE Image Processing, Tech. rep., research report N 94–01, I3S, University of Nice-Sophia Antipolis.
Fessler, J. A. (1994). Penalized Weighted Least-Squares Image for Positron Emission Tomography. IEEE Trans. Med. Imaging, 13:290–300.
Geman, D. and Yang, C. (1995). Nonlinear Image Recovery with Half-Quadratic Regularisation. IEEE Trans. Image Processing, 4:932–946.
Geman, S. and Reynolds, G. (1992). Constrained Restoration and the Recovery of Discontinuities. IEEE Trans. Pattern Anal., 14:367–383.
Grangeat, P. (1991). Mathematical Framework of Cone-Beam Reconstruction via the First Derivative of the Radon Transform. Mathematical Methods in Tomography, ed. G. T. Herman, A. K. Louis and F. Natterer, Berlin: Springer, pages 66–97.
Grangeat, P., Guillemaud, R., Rizo, P., Sauze, R., Donner, Q., and Gorius, J.-P. (1993). Cone-Beam SPECT with a Tilted Detector. Computerized Medical Imaging and Graphics, pages 279–287.
Green, P. J. (1990). Bayesian Reconstruction from Emission Tomography Data Using a Modified EM Algorithm. IEEE Trans. Med. Imaging., 9:84–93.
Gullberg, G. T. (1990). Estimation of Geometrical Parameters and Collimator Evaluation for Cone Beam Tomography. Med. Phys., 17:264–272.
Hadamard, J. (1923). Lectures on the Cauchy Problem in Linear Partial Differential Equation. Yale University Press, New Haven.
Hebert, T. and Leahy, R. (1990). A Generalized EM Algorithm for 3D Bayesian Reconstruction from Poisson Data Using Gibbs Prior. IEEE Trans. Med. Imaging, 8:194–202.
Koulibaly, P. M., Darcourt, J., Charbonnier, P., Migneco, O., Barlaud, M., and BlancFéraud, L. (1995). Comparaison du MAP-EM OSL et d’ARTUR : deux algorithmes déterministes de reconstruction en tomographie d’émission. ITBM, 16:377–390.
Li, J., Jaszczak, R. J., Greer, K. L., and Coleman, R. E. (1994a). Implementation of an Accelerated Iterative Algorithm for Cone-Beam SPECT. Phys. Med. Biol., 39:643–653.
Li, J., Jaszczak, R. J., Turkington, T. G., Metz, C. E., Gilland, D. R., Greer, K. L., and Coleman, R. E. (1994b). An Evaluation of Lesion Detectability with Cone-Beam, Fan-Beam and Parallel Beam Collimation in SPECT by Continuous ROC Study. J. Nucl. Med., 35:135–140.
Li, J., Jaszczak, R. J., Wang, H., Greer, K. L., and Coleman, R. E. (1993). Determination of Both Mechanical and Electronic Shifts in Cone Beam SPECT. Phys. Med. Biol., 38:743–754.
Manglos, S. H. (1992). Truncation Artifact Suppression in Cone-Beam Radionuclide Transmission CT Using Maximum Likelihood Techniques: Evaluation with Human Subjects. Phys. Med. Biol., 37:549–562.
Manglos, S. H., Jaszczak, R. J., and Floyd, C. E. (1989). Maximum Likelihood Reconstruction for Cone-Beam SPECT: Development and Initial Tests. Phys. Med. Biol., 34:1947–1957.
Saint-Felix, D., Trousset, Y., Picard, C., Ponchut, C., Romeas, R., and Rongée, A. (1994). In Vivo Evaluation of a New System for 3D Computerized Angiography. Phys. Med. Biol, 39:583–595.
Stegen, M., Wanet, P., Metello, L., and Rubinstein, M. (1995). Improving Sensitivity of Thyroid Scintigraphy Using Pinhole SPECT. Eur. J. Nuc. Med., 22:745. (abstract).
Stoddart, H. A. and Stoddart, H. F. (1992). New multi-dimensional reconstructions for the 12-detector, scanned focal point, single-photon tomograph. Phys. Med. Biol., 37:579–586.
Tournier, E., Mestais, C., and Peyret, O. (1994). Le compromis sensibilité-résolution, méthodes de collimation, caméras multi-têtes, méthodes tomographiques. Médecine Nucléaire, 18:317–321.
Trousset, Y., Saint-Felix, D., Rougée, A., and Chardenon, C. (1990). Multiscale ConeBeam X-Ray Reconstruction. presented at SPIE Medical Imaging IV (Newport Beach).
Zeng, G. L., Gullberg, G. T., Tsui, B. M. W., and Terry, J. A. (1991). Three-Dimensional Iterative Reconstruction Algorithms with Attenuation and Geometric Point Response Correction. IEEE Trans. Nucl. Sci., 38:693–702.
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Laurette, I. et al. (1996). Cone-Beam Algebraic Reconstruction Using Edge-Preserving Regularization. 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_5
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DOI: https://doi.org/10.1007/978-94-015-8749-5_5
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