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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 1
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Articles

On the approximate inverse method in SPECT image reconstruction

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Pages 121-132 | Received 30 Aug 2017, Accepted 13 Jun 2018, Published online: 27 Jun 2018

References

  • Novikov RG. An inversion formula for the attenuated X-ray transformation. Ark Mat. 2002;40:145–167. doi: 10.1007/BF02384507
  • Natterer F. Inversion of the attenuated Radon transform. Inverse Probl. 2001;17:113–119. doi: 10.1088/0266-5611/17/1/309
  • Boman J, Strömberg JO. Novikov's inversion formula for the attenuated Radon transform-a new approach. J Geom Anal. 2004;14:185–198. doi: 10.1007/BF02922067
  • 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. doi: 10.1080/00036811.2015.1064523
  • Tretiak O, Metz C. The exponential Radon transform. SIAM J Appl Math. 1980;39:341–354. doi: 10.1137/0139029
  • Rullgard H. An explicit inversion formula for the exponential Radon transform using data from 180 degrees. Ark Mat. 2004;42:353–362. doi: 10.1007/BF02385485
  • Wang JP. Inversion and property characterization on generalized transform of Radon type. Acta Math Sci. 2011;31:636–643. Chinese.
  • Shen ZJ, Wang JP. The research of complex analytic method in spect image reconstruction. Appl Anal. 2014;93(11):2451–2461. doi: 10.1080/00036811.2014.930824
  • Puro A. Magnetophotoelasticity as parametric tensor field tomography. Inverse Probl. 1998;14:1315–1330. doi: 10.1088/0266-5611/14/5/015
  • You J. The attenuated Radon transform with complex coefficients. Inverse Probl. 2007;23(5):1963–1971. doi: 10.1088/0266-5611/23/5/010
  • 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
  • Du LL, Li J, Wang JP. The analysis study on nonlinear iterative methods for inverse problems. Appl Anal. 2017;96(6):925–935. doi: 10.1080/00036811.2016.1167190
  • Backus GE, Gilbert JF. Numerical applications of a formalism for geophysical inverse problems. Geophys J R Astron Soc. 1967;13(1–3):247–276. doi: 10.1111/j.1365-246X.1967.tb02159.x
  • 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. Approximate inverse for linear and some nonlinear problems. Inverse Probl. 1996;12:175–190. doi: 10.1088/0266-5611/12/2/005
  • 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(2):025002. doi: 10.1088/1361-6420/33/2/025002
  • Louis AK. Inverse und schlecht gestellte Probleme. Stuttgart:Teubner; 1989.
  • Natterer F. Error bounds for Tikhonov regularization in Hilbert spaces. Appl Anal. 1984;18:29–37. doi: 10.1080/00036818408839508
  • Natterer F. The mathematics of computerized tomography. New York (NY): Wiley; 1986.
  • Rullgård H. Stability of the inverse problem for the attenuated Radon transform with 180° data. Inverse Probl. 2004;20:781–797. doi: 10.1088/0266-5611/20/3/008
  • Cody WJ, Paciorek KA, Thacher HC. Chebyshev approximations for Dawson's integral. Math Comput. 1970;24:171–178.

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