Image Reconstruction from Fan-Beam Projections without Back-Projection Weight in a 2-D Dynamic CT: Compensation of Time-Dependent Rotational, Uniform Scaling and Translational Deformations

DOI: 10.4236/ojmi.2013.34021   PDF   HTML     3,811 Downloads   5,995 Views   Citations


In a dynamic CT, the acquired projections are corrupted due to strong dynamic nature of the object, for example: lungs, heart etc. In this paper, we present fan-beam reconstruction algorithm without position-dependent backprojection weight which compensates for the time-dependent translational, uniform scaling and rotational deformations occurring in the object of interest during the data acquisition process. We shall also compare the computational cost of the proposed reconstruction algorithm with the existing one which has position-dependent weight. To accomplish the objective listed above, we first formulate admissibility conditions on deformations that is required to exactly reconstruct the object from acquired sequential deformed projections and then derive the reconstruction algorithm to compensate the above listed deformations satisfying the admissibility conditions. For this, 2-D time-dependent deformation model is incorporated in the fan-beam FBP reconstruction algorithm with no backprojection weight, assuming the motion parameters being known. Finally the proposed reconstruction algorithm is evaluated with the motion corrupted projection data simulated on the computer.

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A. V. Narasimhadhan, A. Sharma and D. Mistry, "Image Reconstruction from Fan-Beam Projections without Back-Projection Weight in a 2-D Dynamic CT: Compensation of Time-Dependent Rotational, Uniform Scaling and Translational Deformations," Open Journal of Medical Imaging, Vol. 3 No. 4, 2013, pp. 136-143. doi: 10.4236/ojmi.2013.34021.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Kachelriess and W. A. Kalender, “Electrocardiogram-Correlated Image Reconstruction from Subsecond Spiral Computed Tomography Scans of the Heart,” Medical Physics, Vol. 25, 1998, pp. 2417-2431.
[2] T. Flohr and B. Ohnesorge, “Heart Rate Adaptative Optimization of Spatial and Temporal Resolution for Electrocardiogram Gated Multislice Spiral CT of the Heart,” Journal of Computer Assisted Tomography, Vol. 25, No. 6, 2001, pp. 907-923.
[3] D. R. Gilland, B. A. Mair, J. E. Bowsher and R. J. Jaszczak, “Simultaneous Reconstruction and Motion Estimation for Gated Cardiac ECT,” IEEE Transactions on Nuclear Science, Vol. 49, No. 5, 2002, pp. 2344-2349.
[4] J. De Murcia, “Reconstruction d’Images Cardiaques en Tomographie d’Emission Monophotonique a I’Aide de Modeles Spatio Temporels,” PhD Thesis, Institut National Polytechnique de Grenoble, 1996.
[5] C. Blondel, R. Vaillant, G. Malandain and N. Ayache, “3D Tomographic Reconstruction of Coronary Arteries Using a Precomputed 4D Motion Field,” Proceedings of 7th International Conference on Fully 3D Reconstruction in Radiology and Nuclear Medicine, Saint Malo, July 2003.
[6] S. Bonnet, A. Koenig, S. Roux, P. Hugonnard, R. Guillenaud and P. Grangeat, “Dynamic X-Ray Computed Tomography,” Proceedings of the IEEE, Vol. 91, No. 10, 2003, pp. 1574-1587.
[7] C. J. Ritchie, C. R. Crawford, J. D. Gowvin, K. F. King and Y. Kim, “Correction of Computed Tomography Motion Artefacts Using Pixel-Specific Back-Projection,” IEEE Transactions on Medical Imaging, Vol. 15, No. 3, 1996, pp. 333-342.
[8] P. Grangeat, A. Koenig, T. Rodet and S. Bonnet, “Theoretical Framework for a Dynamic Cone-Beam Reconstruction Algorithm Based on a Dynamic Particle Model,” Physics in Medicine and Biology, Vol. 47, No. 15, 2002, pp. 2611-2625.
[9] W. Lu and T. R. Mackie, “Tomographic Motion Detec- tion and Correction Directly in Sinogram Space,” Physics in Medicine and Biology, Vol. 47, No. 8, 2002, pp. 1267- 1284.
[10] S. Roux, L. Desbat, A. Koeing and P. Grangeat, “Exact Reconstruction in 2D Dynamic CT Compensation of Time-Dependent Affine Deformations,” Physics in Medicine and Biology, Vol. 49, No. 11, 2004, pp. 2169-2182.
[11] F. Noo, M. Defrise, R. Clackdoyle and H. Kudo, “Image Reconstruction from Fan Beam Projections on Less than a Short-Scan,” Physics in Medicine and Biology, Vol. 47, No. 14, 2002, pp. 2525-2546.
[12] A. Katsevich, “An Improved Exact Filtered Backprojection Algorithm for Spiral Computed Tomography,” Advances in Applied Mathematics, Vol. 32, No. 4, 2004, pp. 625-825.
[13] F. Dennerlein, F. Noo, J. Hornegger and G. Lauritsch, “Fan-Beam Filtered-Backprojection Reconstruction without Backprojection Weight,” Physics in Medicine and Bi- ology, Vol. 52, No. 11, 2007, pp. 3227-3240.
[14] C. Hamaker, K. T. Smith, D. C. Solmon and S. L. Wagner, “The Divergent Beam X-Ray Transform,” Rockey Mountain Journal of Mathematics, Vol. 10, No. 1, 1980, pp. 253-283.
[15] A. C. Kak and M. Slaney, “Principles of Computerized Tomographic Imaging,” IEEE Press, New York, 1987.
[16] G. L. Zeng, “Nonuniform Noise Propagation by Using the Ramp Filter in Fan-Beam Computed Tomography,” IEEE Transactions on Medical Imaging, Vol. 23, No. 6, 2004, pp. 690-695.
[17] X. Pan and L. Yu, “Image Reconstruction with Shift-Variant Filtration and Its Implication for Noise and Resolution Properties in Fan-Beam Computed Tomography,” Medical Physics, Vol. 30, 2003, pp. 590-600.
[18] J. You and G. L. Zeng, “Hilbert Transform Based FBP Algorithm for Fan-Beam CT Full and Partial Scans,” IEEE Transactions on Medical Imaging, Vol. 26, No. 2, 2007, pp. 190-199.
[19] A. V. Narasimhadhan and K. Rajgopal, “FDK-Type Algorithms with no Backprojection Weight for Circular and Helical Cone-Beam CT,” International Journal of Biomedical Imaging, Vol. 2012, 2012.
[20] H. Kudo, F. Noo, M. Defrise and R. Clackdoyle, “New Super Short-Scan Algorithm for Fan-Beam and Cone-Beam Reconstruction,” Proceedings of IEEE MIC, M5-3, 2002, pp. 902-906.
[21] A. A. Zamyatin, K. Taguchi and M. D. Silver, “Practical Hybrid Convolution Algorithm for Helical CT Reconstruction,” IEEE Transactions on Nuclear Science, Vol. 53, No. 1, 2006, pp. 167-174.

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