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Articles

CT image reconstruction algorithms based on the Hanke Raus parameter choice rule

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Pages 87-103 | Received 02 Mar 2017, Accepted 30 May 2019, Published online: 14 Jun 2019

References

  • Natterer F. The mathematics of computerized tomography. Philadelphia (PA): SIAM; 2001.
  • Burger M, Müller J, Papoutsellis E, et al. Total variation regularization in measurement and image space for PET reconstruction. Inverse Probl. 2014;30:105003.
  • Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer; 1996.
  • Schuster T, Kaltenbacher B, Hofmann B, et al. Regularization methods in Banach spaces: radon series on computational and applied mathematics. Berlin: De Gruyter; 2012.
  • Guan H, Gordon R. Computed tomography using algebraic reconstruction techniques (ARTs) with different projection access schemes: a comparison study under practical situations. Phys Med Biol. 1996;41:1727–1743. doi: 10.1088/0031-9155/41/9/012
  • Xu X, Liow J, Strother SC. Iterative algebraic reconstruction algorithms for emission computed tomography: a unified framework and its application to positron emission tomography. Med Phys. 1993;20:1675–1684. doi: 10.1118/1.596954
  • Andersen AH, Kak AC. Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm. Ultrason Imaging. 1984;6:81–94. doi: 10.1177/016173468400600107
  • Kolehmainen V, Lassas M, Siltanen S. Limited data x-ray tomography using nonlinear evolution equations. SIAM J Sci Comput. 2008;30:1413–1429. doi: 10.1137/050622791
  • Sidky EY, Pan XC. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol. 2008;53:4777–4807. doi: 10.1088/0031-9155/53/17/021
  • Vandeghinste B, Goossens B, Beenhouwer JD, et al. Split-Bregman-based sparse-view CT reconstruction. Fully 3D 2011 proceedings. p. 431–434.
  • Chen ZQ, Jin X, Li L, et al. A limited-angle CT reconstruction method based on anisotropic TV minimization. Phys Med Biol. 2013;58:2119–2141. doi: 10.1088/0031-9155/58/7/2119
  • Anzengruber SW, Hofmann B, Mathé P. Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces. Appl Anal. 2014;93:1382–1400. doi: 10.1080/00036811.2013.833326
  • Hansen PC, O'Leary DP. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput. 1993;14:1487–1503. doi: 10.1137/0914086
  • Kindermann S, Neubauer A. On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization. Inverse Probl Imag. 2008;2:291–299. doi: 10.3934/ipi.2008.2.291
  • Hanke M, Raus T. A general heuristic for choosing the regularization parameter in ill-posed problems. SIAM J Sci Comput. 1996;17:956–972. doi: 10.1137/0917062
  • Jin B, Lorenz DA. Heuristic parameter-choice rules for convex variational regularization based on error estimates. SIAM J Numer Anal. 2010;48:1208–1229. doi: 10.1137/100784369
  • Jin Q. Hanke-Raus heuristic rule for variational regularization in Banach spaces. Inverse Probl. 2016;32:085008.
  • Kashef J, Moosmann J, Stotzka R, et al. TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data. Opt Express. 2015;23(5):5368–5387. doi: 10.1364/OE.23.005368
  • Vogel CR. Non-convergence of the L-curve regularization parameter selection method. Inverse Probl. 1996;12(4):535–547. doi: 10.1088/0266-5611/12/4/013
  • Burger M, Osher S. Convergence rates of convex variational regularization. Inverse Probl. 2004;20(5):1411–1421. doi: 10.1088/0266-5611/20/5/005
  • Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pur Appl Math. 2004;57:1413–1457. doi: 10.1002/cpa.20042
  • Figueiredo MAT, Nowak RD, Wright SJ. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J-STSP. 2008;1:586–597.
  • Hale ET, Yin W, Zhang Y. Fixed-point continuation for ℓ1-minimization: methodology and convergence. SIAM J Optim. 2008;19:1107–1130. doi: 10.1137/070698920
  • Griesse R, Lorenz DA. A semismooth Newton method for Tikhonov functionals with sparsity constraints. Inverse Probl. 2008;24:035007. doi: 10.1088/0266-5611/24/3/035007
  • Jin B, Lorenz D, Schifler S. Elastic-net regularization: error estimates and active set methods. Inverse Probl. 2009;25:1595–1610.
  • Beck A, Teboulle M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE T Image Process. 2009;18:2419–2434. doi: 10.1109/TIP.2009.2028250
  • Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci. 2009;2:183–202. doi: 10.1137/080716542
  • Goldstein T, Osher S. The split Bregman method for ℓ1-regularized problems. SIAM J Imaging Sci. 2009;2:323–343. doi: 10.1137/080725891
  • Liu X, Huang L. Split Bregman iteration algorithm for total bounded variation regularization based image deblurring. J Math Anal Appl. 2010;372:486–495. doi: 10.1016/j.jmaa.2010.07.013
  • Liu J, Huang TZ, Selesnick IW, et al. Image restoration using total variation with overlapping group sparsity. Inform Sci. 2015;295:232–246. doi: 10.1016/j.ins.2014.10.041
  • Sisniega A, Abascal J, Abella M, et al. Iterative Dual-Energy material decomposition for slow kVp switching: a compressed sensing approach. In: XIII Mediterranean Conference on Medical and Biological Engineering and Computing 2013. Cham: Springer; 2014. p. 491–494.
  • Nien H, Fessler JA. A convergence proof of the split Bregman method for regularized least-squares problems. Mathematics. arXiv preprint, 2014, arXiv:1402.4371.
  • Jiao Y, Jin Q, Lu X, et al. Alternating direction method of multipliers for linear inverse problems. SIAM J Numer Anal. 2016;54:2114–2137. doi: 10.1137/15M1029308
  • Wang Z, Bovik AC, Sheikh HR, et al. Image quality assessment: from error visibility to structural similarity. IEEE T Image Process. 2004;13:600–612. doi: 10.1109/TIP.2003.819861
  • Fan Q, Jiao Y, Lu X. A primal dual active set algorithm with continuation for continuation for compressed sensing. IEEE T Signal Process. 2014;62:6276–6285. doi: 10.1109/TSP.2014.2362880

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