References
[1] F. Noo, R. Clackdoyle, and J. D. Pack. “A two-step Hilbert transform method for 2D image reconstruction,” Physics in Medicine & Biology, vol. 49, no. 17, p. 3903, 2004.
[2] M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo. “Truncated Hilbert transform and image reconstruction from limited tomographic data,” Inverse Problems, vol. 22, no. 3, p. 1037, 2006.
[3] A. Katsevich. “Singular value decomposition for the truncated Hilbert transform,” Inverse Problems, vol. 26, no. 11, p. 115011, 2010.
[4] A. Katsevich. “Singular value decomposition for the truncated Hilbert transform: part II,” Inverse Problems, vol. 27, no. 7, p. 075006, 2011.
[5] E. Y. Sidky and X. Pan. “Recovering a compactly supported function from knowledge of its Hilbert transform on a finite interval,” IEEE Signal Processing Letters, vol. 12, no. 2, pp. 97-100, 2005.
[6] Y. Ye, H. Yu, Y. Wei, G. Wang, et al. “A general local reconstruction approach based on a truncated Hilbert transform,” Interna-tional Journal of Biomedical Imaging, vol. 2007, 2007.
[7] J. You and G. L. Zeng. “Explicit finite inverse Hilbert transforms,” Inverse Problems, vol. 22, no. 3, p. L7, 2006.
[8] G. L. Zeng. “Image reconstruction via the finite Hilbert transform of the derivative of the backprojection,” Medical Physics, vol. 34, no. 7, pp. 2837-2843, 2007.
[9] G. L. Zeng, J. You, Q. Huang, and G. T. Gullberg. “Two finite inverse Hilbert transform formulae for region-of-interest tomogra-phy,” International Journal of Imaging Systems and Technology, vol. 17, no. 4, pp. 219-223, 2007.
[10] A. Coussat, S. Rit, R. Clackdoyle, M. Defrise, L. Desbat, and J. M. L´etang. “ROI CT reconstruction combining analytic inversion of the finite Hilbert transform and SVD,” in Sixth international conference on image formation in X-ray computed tomography, 2020, pp. 526-529.
[11] A. Katsevich, M. Bertola, and A. Tovbis. “Inversion formula and range conditions for a linear system related with the multi-interval finite Hilbert transform in L2,” Mathematische Nachrichten, vol. 294, no. 8, pp. 1523-1546, 2021.
[12] Q. Chen, N. Huang, S. Riemenschneider, and Y. Xu. “A B-spline approach for empirical mode decompositions,” Advances in Computational Mathematics, vol. 24, pp. 171-195, 2006.
[13] C. A. Micchelli, Y. Xu, and B. Yu. “On computing with the Hilbert spline transform,” Advances in Computational Mathematics, vol. 38, pp. 623-646, 2013.
[14] G. P. Curbera, S. Okada, and W. J. Ricker. “Inversion and extension of the finite Hilbert transformon (-1, 1),” Annali di Matematica Pura ed Applicata (1923-), vol. 198, no. 5, pp. 1835-1860, 2019.
[15] F. W. King. Hilbert Transforms. Cambridge University Press, 2009, vol. 1.
[16] A. Robinson and J. A. Laurmann. Wing Theory. Cambridge University Press, 2013.
[17] F. G. Tricomi. Integral Equations. Cambridge University Press, 1957.
[18] G. F. Carrier, M. Krook, and C. E. Pearson. Functions of a Complex Variable: Theory and Technique. SIAM, 2005.
[19] R. Kenwal. Linear Integral Equations Theory and Technique, Academic Press, 1971.
[20] T. Hartmann and E. Stephan. “Rates of convergence for collocation with Jacobi polynomials for the airfoil equation,” Journal of Computational and Applied Mathematics, vol. 51, no. 2, pp. 179-191, 1994.
[21] C. De Boor. Splines as Linear Combinations of B-splines: A Survey. University of Wisconsin Madison. Mathematics Research Center, 1976.
[22] C. A. Micchelli, Y. Xu, and H. Zhang. “On translation invariant operators which preserve the B-spline recurrence,” Advances in Computational Mathematics, vol. 28, no. 2, pp. 157-169, 2008.