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Sinogram Interpolation Method for Sparse-Angle Tomography

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DOI: 10.4236/am.2014.53043    4,608 Downloads   6,800 Views   Citations


In sparse-angle X-ray tomography reconstruction, where only a small number of projection images are taken around the object, appropriate sinogram interpolation has a significant impact on image quality. A novel sinogram interpolation method is introduced for extreme sparse tomographic reconstruction where only nine measured projection images are available. The sinogram is interpolated by solving characteristics of the so-called warps, which can be considered as approximation sine waves in a limited region. The numerical evidence suggests that this approach gives superior results over standard interpolation methods when the tomographic data are extremely sparse and noisy.

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The authors declare no conflicts of interest.

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M. Kalke and S. Siltanen, "Sinogram Interpolation Method for Sparse-Angle Tomography," Applied Mathematics, Vol. 5 No. 3, 2014, pp. 423-441. doi: 10.4236/am.2014.53043.


[1] R. A. Brooks, G. H. Weiss and A. J. Talbert, “A New Approach to Interpolation in Computed Tomography,” Journal of Computed Assisted Tomography, Vol. 2, No. 5 1978, pp. 577-585.
[2] N. Hyvonen, M. Kalke, M. Lassas, H. Setala and S. Siltanen, “Three-Dimensional X-Ray Imaging Using Hybrid Data Collected with a Digital Panoramic Device,” Inverse Problems and Imaging, Vol. 4, No. 2, 2010, pp. 257-271.
[3] M. Rantala, S. Vanska, S. Jarvenpaa, M. Kalke, M. Lassas, J. Moberg and S. Siltanen, “Wavelet-Based Reconstruction for Limited-Angle X-Ray Tomography,” IEEE Transactions on Medical Imaging, Vol. 25, No. 2, 2006, pp. 210-217.
[4] M. Varjonen, “Three-Dimensional Digital Breast Tomosynthesis in the Early Diagnosis and Detection of Breast Cancer,” Springer, Berlin, 2006.
[5] S. Siltanen, V. Kolehmainen, S. Jarvenpaa, J. P. Kaipio, P. Koistinen, M. Lassas, J. Pirttila and E. Somersalo, “Statistical Inversion for X-Ray Tomography with Few Radiographs I: General Theory,” Physics in Medicine and Biology, Vol. 48, No. 10, 2003, pp. 1437-1463.
[6] V. Kolehmainen, S. Siltanen, S. Jarvenpaa, J. P. Kaipio, P. Koistinen, M. Lassas, J. Pirttila and E. Somersalo, “Statistical Inversion for Medical X-Ray Tomography with Few Radiographs: II. Application to Dental Radiology,” Physics in Medicine and Biology, Vol. 48, No. 10, 2003, pp. 1465-1490.
[7] V. Kolehmainen, M. Lassas and S. Siltanen, “Limited Data X-Ray Tomography Using Nonlinear Evolution Equations,” SIAM Journal of Scientific Computing, Vol. 30, No. 3, 2008, pp. 1413-1429.
[8] R. L. Webber, R. A. Horton, D. A. Tyndall and J. B. Ludlow, “Tuned Aperture Computed Tomography, (TACT) Theory and Application for Three-Dimensional Dento-Alveolar Imaging,” Dentomaxillofacial Radiology, Vol. 26, No. 1, 1999, pp. 53-62.
[9] A. Cederlund, M. Kalke and U. Welander, “Volumetric Tomography—A New Tomographic Technique for Panoramic Units,” Dentomaxillofacial Radiology, Vol. 38, No. 2, 2009, pp. 104-111.
[10] J. Hsieh, “Computed Tomography: Principles, Design, Artifacts, and Recent Advances,” SPIE Press, Bellingham, 2009.
[11] A. C. Kak and M. Slaney, “Principles of Computerized Tomography,” SIAM, 2001.
[12] R. C. Gonzalez and R. E. Woods, “Digital Image Processing,” 3rd Edition, Pearson Education Inc., Upper Saddle River, 2008.
[13] P. La Riviere, “Noise Properties of Periodic Interpolation Methods with Implications for Few-View Tomography,” IEEE Transactions on Nuclear Science, Vol. 46, No. 3, 1999, pp. 639-645.
[14] S. Schaller, T. Flohr, K. Klingenbeck, J. Krause, T. Fuchs and W. A. Kalender, “Spiral Interpolation Algorithm for Multislice Spiral CT. I. Theory,” IEEE Transactions on Medical Imaging, Vol. 19, No. 9, 2000, pp. 822-834.
[15] Z. Y. Liu and F. Y. Sze, “A Sinogram Restoration Technique for the Hollow Projection Problem in Computer Tomography,” IEEE Proceedings of the 20th Annual International Conference of the Engineering in Medicine and Biology Society, Hong Kong, 29 October-1 November 1998, pp. 656-659.
[16] M. Yazdi and L. Beaulieu, “A Novel Approach for Reducing Metal Artifacts Due to Metallic Dental Implants,” IEEE Nuclear Science Symposium Conference Record, San Diego, 29 October-1 November 2006, pp. 2260-2263.
[17] E. Meyer, F. Bergner, R. Raupach, T. Flohr and M. Kachelriess, “Normalized Metal Artifact Reduction (NMAR) in Computed Tomography,” IEEE Nuclear Science Symposium Conference Record (NSS/MIC), Orlando, 24 October-1 November 2009, pp. 3251-3255.
[18] M. Abdoli, J. R. de Jong, J. Pruim, R. Dierckx and H. Zaidi, “Clough-Tocher Interpolation of Virtual Sinogram in a Delaunay Triangulated Grid Foal Artifact Reduction of PET/CT Images,” IEEE Nuclear Science Symposium and Medical Imaging Conference, Valencia, 23-29 October 2011, pp. 3197-3201.
[19] F. Sze and H. W. Y. Shum, “A Linear Sinogram Extrapolator for Limited Angle Tomography,” 3rd International Conference Signal Processing, Beijing, 14-18 October 1996, pp. 386-389.
[20] D. R. Gilland, R. J. Jaszczak and R. E. Coleman, “Transmission CT Reconstruction for Offset Fan Beam Collimation,” IEEE Transactions on Nuclear Science, Vol. 47, No. 4, 2000, pp. 1602-1606.
[21] L. Baojun and H. Jiang, “Comparison of Reconstruction Algorithms to Extend CT Reconstruction Field-of-View,” IEEE Nuclear Science Symposium Conference Record, 26 October-3 November 2007, pp. 3912-3914.
[22] A. A. Zamyatin and S. Nakanishi, “Sinogram Correction Methods Using Sinogram Decomposition,” IEEE Nuclear Science Symposium Conference Record, 29 October-1 November 2006, pp. 3438-3440.
[23] M. J. Lahart, “Estimation of Reconstructions in Computed Tomography,” Journal of Optical Society of America, Vol. 71, No. 10, 1981, pp. 1155-1161.
[24] C. R. Crawford and A. C. Kak, “Aliasing Artifacts in Computerized Tomography,” Applied Optics, Vol. 18, No. 21, 1979, pp. 3704-3711.
[25] T. Inouye, “Mage Reconstruction with Limited Angle Projection Data,” IEEE Transactions in Nuclear Science, Vol. 21, 1979, pp. 2666-2669.
[26] D. L. Snyder and J. R. Cox, “An Overview of Reconstructive Tomography and Limitations Imposed by a Finite Number of Projections—Reconstruction Tomography in Diagnostic Radiography and Nuclear Medicine,” University Park Press, Baltimore, 1977.
[27] T. Sato, S. Norton, M. Linzer, O. Ikeda and M. Hirama, “Tomographic Image Reconstruction from Limited Projections Using Interactive Revision in Image and Transform Spaces,” Applied Optics, Vol. 20, No. 3, 1981, pp. 395-399.
[28] C. Zhe, B. Parker and D. Feng, “Temporal Compression for Dynamic Positron Emission Tomography via Principal Component Analysis in the Sinogram Domain,” IEEE Nuclear Science Symposium Conference Record, Vol. 4, 2003, pp. 2858-2862.
[29] H. Kostler, “Adaptive Variational Sinogram Interpolation of Sparsely Sampled CT Data,” The 18th International Conference on Pattern Recognition, Hong Kong, Vol. 3, 2006, pp. 778-781.
[30] C. Penbel, M. Kachelrieb, M. Knaup and V. A. Kalender, “Azimuthal Interpolation and Noise Reduction,” IEEE Nuclear Science Symposium Conference Record, Vol. 4, 2005, pp. 1946-1949.
[31] M. Bertram, G. Rose, D. Schafer, J. Wiegert and T. Aach, “Directional Interpolation of Sparsely Sampled Cone-Beam CT Sinogram Data,” Nano to Macro, International Symposium, Arlington, 15-18 April 2004, pp. 928-931.
[32] M. Bertram, J. Wiegert, D. Schafer, T. Aach and G. Rose, “Directional View Interpolation for Compensation of Sparse Angular Sampling in Cone-Beam CT,” IEEE Transactions on Medical Imaging, Vol. 28, No. 7, 2099, pp. 1011-1022.
[33] A. Happonen, “Decomposition of Radon Projections into Stackgrams for Filtering, Extrapolation and Alignment of Sinogram Data,” Tampere University of Technology, 2005.
[34] J. Prince and A. Willsky, “Hierarchical Reconstruction Using Geometry and Sinogram Restoration,” IEEE Transactions on Image Processing, Vol. 2, No. 3, 1993, pp. 401-416.
[35] R. W. Gerchberg, “Super-Resolution through Error Energy Reduction,” Optical Acta, Vol. 21, No. 9, 1974, pp. 709-720.
[36] A. Papoulis, “A New Algorithm in Spectral Analysis and Band-Limited Extrapolation,” IEEE Transactions in Circuits Systems, Vol. 22, 1975, pp. 735-742.
[37] P. La Riviere, P. Xiaochuan and C-M. Kao, “Medical Imaging Applications of Effectively Multi-Dimensional Interpolation,” Nuclear Science Symposium, Vol. 2, 1999, pp. 1023-1027.
[38] D. Bin, J. Lia and Z. Shen, “X-Ray CT Image Reconstruction via Wavelet Frame Based Regularization and Radon Domain Inpainting,” Journal of Scientific Computing, Vol. 54, No. 2-3, 2013, pp. 333-349.
[39] G. Golub and C. F. Van Loan, “Matrix Computations,” 3rd Edition, The John Hopkins University Press, Baltimore, 1996.
[40] G. B. Arfken and H. J. Weber, “Mathematical Methods for Physicists,” Harcourt/Academic Press, San Diego, 2001.
[41] J. Kaipio and E. Somersalo, “Statistical and Computational Inverse Problems,” Springer-Verlag, New York, 2005.
[42] F. Natterer, “The Mathematics of Computerized Tomography,” John Wiley and Sons Ltd., Chichester; B. G. Teubner, Stuttgart, 1986.
[43] E. Constantino and K. Ozanyan, “Sinogram Enhancement for Tomographic Sensing Systems with Limited Resources,” IEEE Conference on Sensors, Daegu, 22-25 October 2006, pp. 514-517.
[44] E. Constantino and K. Ozanyan, “Tomographic Imaging of Surface Deformation from Scarce Measurements via Sinogram Recovery,” IEEE Sensors Journal, Vol. 9, No. 4, 2009, pp. 399-410.
[45] K. C. Tam, J. W. Eberhard and K. W. Mitchell, “Incomplete-Data CT Image Reconstructions in Industrial Applications,” IEEE Transactions on Nuclear Science, Vol. 37, No. 3, 1990, pp. 1490-1499.
[46] S. Ha, S. Matej, M. Ispiryan and K. Müller, “GPU-Accelerated Forward and Backward Projection with Spatially Varying Kernels in 3D DIRECT TOF PET Reconstruction,” IEEE Transactions on Nuclear Science, Vol. 60, No. 1, 2013, pp. 166-173.
[47] K. S. Kyung and C. Y. Jong, “Fast Implementation of Fully Iterative Scatter Corrected OSEM for HRRT Using GPU,” IEEE Nuclear Science Symposium Conference Record (NSS/MIC), Knoxville, 30 October-6 November 2010, pp. 3330-3332.
[48] V. Kolehmainen, A. Vanne, S. Siltanen, S. Jarvenpaa, J. P. Kaipio, M. Lassas and M. Kalke, “Parallelized Bayesian Inversion for Three-Dimensional Dental X-Ray Imaging,” IEEE Transactions on Medical Imaging, Vol. 25, No. 2, 2006, pp. 218-228.
[49] L. Goldman and J. Fowlkes, “Categorical Course in diagnostic Radiology: CT and US Cross-Sectional Imaging,” RSNA, Oak Brook, 2000.
[50] J. H. Veldkamp, R. M. S. Joemai, A. J. van der Molen and J. Geleijns, “Development and Validation of Segmentation and Interpolation Techniques in Sinograms for Metal Artifact Suppression in CT,” Medical Physics, Vol. 37, No. 2, 2010, pp. 620-628.
[51] S. Karimi, P. Cosman, C. Wald and H. Martz, “Using Segmentation in CT Metal Artifact Reduction,” IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI), Santa Fe, 22-24 April 2012, pp. 9-12.

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