References
- Natterer F. The mathematics of computerized tomography. New York (NY): Wiley; 1986.
- Wang JP, Du JY. A note on singular value decomposition for Radon transform in Rn. Acta Math Sci. 2002;22(3):311–318. doi: 10.1016/S0252-9602(17)30300-4
- Shen ZJ, Wang JP. The improved reconstruction method for nonuniform attenuated SPECT data. Acta Math Sci. 2015;35B(3):527–538. doi: 10.1016/S0252-9602(15)30001-1
- Tretiak O, Metz CE. The exponential Radon transform. SIAM J Appl Math. 1980;39:341–354. doi: 10.1137/0139029
- Novikov RG. An inversion formula for the attenuated X-ray transformation. Ark Math. 2002;40:145–167. doi: 10.1007/BF02384507
- Kunyansky LA. A new SPECT reconstruction algorithm based on Novikov's explicit inversion formula. Inverse Probl. 2001;17:293–306. doi: 10.1088/0266-5611/17/2/309
- Natterer F. Inversion of the attenuated Radon transform. Inverse Probl. 2001;17:113–119. doi: 10.1088/0266-5611/17/1/309
- Natterer F. The attenuated Radon transform for complex attenuation. Technical Report, Fachbereich Mathematik und Informatik, Universität Münster; 2007.
- Louis AK, Maass P. A mollifier method for linear operator equations of the first kind. Inverse Probl. 1990;6(3):427–440. doi: 10.1088/0266-5611/6/3/011
- Louis AK. Combining image reconstruction and image analysis with an application to 2D-tomography. SIAM J Imaging Sci. 2008;1:188–208. doi: 10.1137/070700863
- Louis AK. Feature reconstruction in inverse problems. Inverse Probl. 2011;27:065010.
- Louis AK. A unified approach to regularization methods for linear ill-posed problems. Inverse Probl. 1999;15:489–498. doi: 10.1088/0266-5611/15/2/009
- Rigaud G, Lakhal A. Approximate inverse and Sobolev estimates for the attenuated Radon transform. Inverse Probl. 2015;31(10):105010. doi: 10.1088/0266-5611/31/10/105010
- Rigaud G, Lakhal A. Image and feature reconstruction for the attenuated Radon transform via circular harmonic decomposition of the kernel. Inverse Probl. 2015;31(2):025007. doi: 10.1088/0266-5611/31/2/025007
- Sharafutdinov VA. The Reshetnyak formula and Natterer stability estimates in tensor tomography. Inverse Probl. 2017;33:025002. doi: 10.1088/1361-6420/33/2/025002
- Stein EM, Weiss D. Introduction to Fourier analysis on Euclidean spaces. Princeton (NJ): Princeton University Press; 1971.
- Louis AK. Inverse und schlecht gestellte Probleme. Stuttgart: Teubner; 1989.
- Natterer F. Error bounds for Tikhonov regularization in Hilbert scales. Appl Anal. 2007;18:29–37. doi: 10.1080/00036818408839508
- Cody WJ, Paciorek KA, Thacher HC. Chebyshev approximations for Dawson's integral. Math Comput. 1970;24:171–178.
- Lu JK. Boundary value problems for analytic functions. Singapore: World Scientific; 1993.
- Wang YF, Han PJ, Wang YJ. On Riemann problem of automorphic polyanalytic functions connected with a rotation group. Complex Var Elliptic Equ. 2015;60:1033–1057. doi: 10.1080/17476933.2014.992424
- Begehr H, Du JY, Wang YJ. A Dirichlet problem for polyharmonic functions. Ann Mat Pura Appl. 2008;187(3):435–457. doi: 10.1007/s10231-007-0050-5