A new complex approach towards approximate inverse and generalized Radon transform

References

• Rullgård H . Stability of the inverse problem for the attenuated Radon transform with 180π data. Inverse Probl. 2004;20:781–797.
   Web of Science ®Google Scholar
• Natterer F . The mathematics of computerized tomography. New York (NY): John Wiley and Sons; 1986.
   Google Scholar
• Shi TT , Wang JP . Reconstruction of the attenuated Radon transform in π-scheme short-scan SPECT. Acta Math Sci. 2013;33B(6):1615–1626.
   Google Scholar
• Schuster T . The 3D Doppler transform: elementary properties and computation of reconstruction kernels. Inverse Probl. 2000;16:701–722.
   Web of Science ®Google Scholar
• Sparr G , Stråhlén K , Lindström K , et al . Doppler tomography for vector fields. Inverse Probl. 1995;11:1051–1061.
   Web of Science ®Google Scholar
• Wang JP , Du JY . A note on singular value decomposition for Radon transform in ℝn. Acta Math Sci. 2002;22B(3):311–318.
   Google Scholar
• Tretiak O , Metz C . The exponential Radon transform. SIAM J Appl Math. 1980;39:341–354.
   Web of Science ®Google Scholar
• Natterer F . Inversion of the attenuated Radon transform. Inverse Probl. 2001;17:113–119.
   Web of Science ®Google Scholar
• Novikov RG . An inversion formula for the attenuated X-ray transformation. Ark Math. 2002;40:145–167.
   Web of Science ®Google Scholar
• Novikov RG . On the range characterization for the two-dimensional attenuated X-ray transformation. Inverse Probl. 2002;18:677–700.
   Web of Science ®Google Scholar
• Arbuzov EV , Bukhgeim AL , Kazantsev SG . Two-dimensional tomography problems and the theory of A-analytic functions. Sib Adv Math. 1998;8:1–20.
   Google Scholar
• Zhao YY , Ye LY , Wang JP . The inverse problem reconstruction approach for single-photon emission computed tomography imaging. Appl Anal. 2016;95(6):1389–1401.
   Web of Science ®Google Scholar
• Kuchment P , Shneiberg I . Some inversion formulas in the single photon emission computed tomography. Appl Anal. 1991;53:221–231.
   Google Scholar
• Panchenko AN . Inverse source problem of radiative transfer: a special case of the attenuated Radon transform. Inverse Probl. 1993;9:321–337.
   Web of Science ®Google Scholar
• Sharafutdinov VA . On emission tomography of inhomogeneous media. SIAM J Appl Math. 1995;55:707–718.
   Web of Science ®Google Scholar
• Shen ZJ , Wang JP . The research of complex analytic method in spect image reconstruction. Appl Anal. 2014;93(11):2451–2461.
   Web of Science ®Google Scholar
• Backus G , Gilbert F . The resolving power of growth earth data. Geophys J R Astron Soc. 1968;16:169–205.
   Web of Science ®Google Scholar
• Likht MK . On the calculation of functionals in the solution of linear equations of the first kind. USSR Comput Math Math Phys. 1967;7:271–278.
   Google Scholar
• Louis AK . A unified approach to regularization methods for linear ill-posed problems. Inverse Probl. 1999;15:489–498.
   Web of Science ®Google Scholar
• Louis AK , Maass P . A mollifier method for linear operator equations of the first kind. Inverse Probl. 1990;6:427–440.
   Web of Science ®Google Scholar
• Louis AK . Combining image reconstruction and image analysis with an application to 2D-tomography. SIAM J Imag Sci. 2008;01:188–208.
   Web of Science ®Google Scholar
• Rigaud G , Lakhal A . Approximate inverse and Sobolev estimates for the attenuated Radon transform. Inverse Probl. 2015;31(10):105010.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Courdurier M , Monard F , Osses A , et al . Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data. Inverse Probl. 2015;31(9):681–695.
   Web of Science ®Google Scholar
• Louis AK . Feature reconstruction in inverse problems. Inverse Probl. 2011;27:065010.
   Web of Science ®Google Scholar
• Lu JK . Boundary value problems for analytic functions. Singapore: World Scientific; 1993.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Begehr H , Du JY , Wang YF . A Dirichlet problem for polyharmonic functions. Ann Mat Pura Appl. 2008;187(3):435–457.
   Web of Science ®Google Scholar