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Traditional machine learning for limited angle tomography

  • Yixing HuangEmail author
  • Yanye LuEmail author
  • Oliver Taubmann
  • Guenter Lauritsch
  • Andreas Maier
Original Article
  • 102 Downloads

Abstract

Purpose

The application of traditional machine learning techniques, in the form of regression models based on conventional, “hand-crafted” features, to artifact reduction in limited angle tomography is investigated.

Methods

Mean-variation-median (MVM), Laplacian, Hessian, and shift-variant data loss (SVDL) features are extracted from the images reconstructed from limited angle data. The regression models linear regression (LR), multilayer perceptron (MLP), and reduced-error pruning tree (REPTree) are applied to predict artifact images.

Results

REPTree learns artifacts best and reaches the smallest root-mean-square error (RMSE) of 29 HU for the Shepp–Logan phantom in a parallel-beam study. Further experiments demonstrate that the MVM and Hessian features complement each other, whereas the Laplacian feature is redundant in the presence of MVM. In fan-beam, the SVDL features are also beneficial. A preliminary experiment on clinical data in a fan-beam study demonstrates that REPTree can reduce some artifacts for clinical data. However, it is not sufficient as a lot of incorrect pixel intensities still remain in the estimated reconstruction images.

Conclusion

REPTree has the best performance on learning artifacts in limited angle tomography compared with LR and MLP. The features of MVM, Hessian, and SVDL are beneficial for artifact prediction in limited angle tomography. Preliminary experiments on clinical data suggest that the investigation on more features is necessary for clinical applications of REPTree.

Keywords

Machine learning Limited angle tomography Decision tree 

Notes

Compliance with ethical standards

Conflict of interest

Oliver Taubmann and Guenter Lauritsch are with Siemens Healthcare GmbH, Forchheim, Germany. Yixing Huang is supported by Siemens Healthcare GmbH, Forchheim, Germany.

Ethical approval

All data shared in the challenge were fully anonymized. This article does not contain any studies with animals performed by any of the authors.

Informed consent

The clinical data in this paper are from the library of the Low Dose CT Grand Challenge [31]. The library was HIPAAcompliant and built with waiver of informed consent.

Disclaimer

The concepts and information presented in this paper are based on research and are not commercially available.

References

  1. 1.
    Quinto ET (2006) An introduction to X-ray tomography and Radon transforms. Proc Symp APPl Math 63:1CrossRefGoogle Scholar
  2. 2.
    Quinto ET (2007) Local algorithms in exterior tomography. J Comput Appl Math 199(1):141CrossRefGoogle Scholar
  3. 3.
    Grünbaum FA (1980) A study of Fourier space methods for limited angle image reconstruction. Numer Funct Anal Optim 2(1):31CrossRefGoogle Scholar
  4. 4.
    Defrise M, De Mol C (1983) A regularized iterative algorithm for limited-angle inverse Radon transform. Opt Acta: Int J Opt 30(4):403CrossRefGoogle Scholar
  5. 5.
    Qu GR, Lan YS, Jiang M (2008) An iterative algorithm for angle-limited three-dimensional image reconstruction. Acta Math Appl Sin 24(1):157CrossRefGoogle Scholar
  6. 6.
    Qu GR, Jiang M (2009) Landweber iterative methods for angle-limited image reconstruction. Acta Math Appl Sin 25(2):327CrossRefGoogle Scholar
  7. 7.
    Huang Y, Taubmann O, Huang X, Lauritsch G, Maier A (2018) Papoulis–Gerchberg algorithms for limited angle tomography using data consistency conditions. Procs CT Meeting, pp 189–192Google Scholar
  8. 8.
    Louis AK, Törnig W (1980) Picture reconstruction from projections in restricted range. Math Methods Appl Sci 2(2):209CrossRefGoogle Scholar
  9. 9.
    Willsky AS, Prince JL (1990) Constrained sinogram restoration for limited-angle tomography. Opt Eng 29(5):535CrossRefGoogle Scholar
  10. 10.
    Huang Y, Huang X, Taubmann O, Xia Y, Haase V, Hornegger J, Lauritsch G, Maier A (2017) Restoration of missing data in limited angle tomography based on Helgason–Ludwig consistency conditions. Biomed Phys Eng Express 3(3):035015CrossRefGoogle Scholar
  11. 11.
    Davison ME (1983) The ill-conditioned nature of the limited angle tomography problem. SIAM J Appl Math 43(2):428CrossRefGoogle Scholar
  12. 12.
    Louis AK (1986) Incomplete data problems in X-ray computerized tomography: I. Singular value decomposition of the limited angle transform. Numer Math 48(3):251CrossRefGoogle Scholar
  13. 13.
    Sidky EY, Pan X (2008) Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53(17):4777CrossRefGoogle Scholar
  14. 14.
    Ritschl L, Bergner F, Fleischmann C, Kachelrieß M (2011) Improved total variation-based CT image reconstruction applied to clinical data. Phys Med Biol 56(6):1545CrossRefGoogle Scholar
  15. 15.
    Frikel J (2013) Sparse regularization in limited angle tomography. Appl Comput Harmon Anal 34(1):117CrossRefGoogle Scholar
  16. 16.
    Chen Z, Jin X, Li L, Wang G (2013) A limited-angle CT reconstruction method based on anisotropic TV minimization. Phys Med Biol 58(7):2119CrossRefGoogle Scholar
  17. 17.
    Wang T, Nakamoto K, Zhang H, Liu H (2017) Reweighted anisotropic total variation minimization for limited-angle CT reconstruction. IEEE Trans Nucl Sci 64(10):2742CrossRefGoogle Scholar
  18. 18.
    Huang Y, Taubmann O, Huang X, Haase V, Lauritsch G, Maier A (2018) Scale-space anisotropic total variation for limited angle tomography. IEEE Trans Radiat Plasma Med Sci 2(4):307CrossRefGoogle Scholar
  19. 19.
    Wang G (2016) A perspective on deep imaging. IEEE Access 4:8914CrossRefGoogle Scholar
  20. 20.
    Zhu B, Liu JZ, Cauley SF, Rosen BR, Rosen MS (2018) Image reconstruction by domain-transform manifold learning. Nature 555(7697):487CrossRefGoogle Scholar
  21. 21.
    Würfl T, Hoffmann M, Christlein V, Breininger K, Huang Y, Unberath M, Maier AK (2018) Deep learning computed tomography: Learning projection-domain weights from image domain in limited angle problems. IEEE Trans Med Imaging 37Google Scholar
  22. 22.
    Riess C, Berger M, Wu H, Manhart M, Fahrig R, Maier A (2013) TV or not TV? That is the question. Procs Fully 3D: 341–344Google Scholar
  23. 23.
    Hammernik K, Würfl T, Pock T, Maier A (2017) A deep learning architecture for limited-angle computed tomography reconstruction. Procs BVM pp 92–97Google Scholar
  24. 24.
    Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. Procs MICCAI pp 234–241Google Scholar
  25. 25.
    Gu J, Ye JC (2017) Multi-scale wavelet domain residual learning for limited-angle CT reconstruction. Procs Fully 3D:443–447Google Scholar
  26. 26.
    Zeiler MD, Fergus R (2014) Visualizing and understanding convolutional networks. Eur Conf Comput Vis pp 818–833Google Scholar
  27. 27.
    Rosenblatt F (1958) The perceptron: a probabilistic model for information-storage and organization in the brain. Psychol Rev 65:386CrossRefGoogle Scholar
  28. 28.
    Kohonen T (1988) An introduction to neural computing. Neural Netw 1(1):3CrossRefGoogle Scholar
  29. 29.
    Loh WY (2011) Classification and regression trees. Wiley Interdiscip Rev Data Min Knowl Discov 1(1):14CrossRefGoogle Scholar
  30. 30.
    Quinlan JR (1987) Simplifying decision trees. Int J Man Mach Stud 27(3):221CrossRefGoogle Scholar
  31. 31.
    McCollough CH, Bartley AC, Carter RE, Chen B, Drees TA, Edwards P, Holmes DR, Huang AE, Khan F, Leng S, McMillan KL, Michalak GJ, Nunez KM, Yu L, Fletcher JG (2017) Low-dose CT for the detection and classification of metastatic liver lesions: Results of the 2016 low dose CT grand challenge. Med Phys 44(10)Google Scholar
  32. 32.
    Frank E, Hall MA, Witten IH (2016) The WEKA workbench. Online appendix for data mining: practical machine learning tools and techniques (Morgan Kaufmann, 2016)Google Scholar
  33. 33.
    Maier A, Hofmann H, Berger M, Fischer P, Schwemmer C, Wu H, Müller K, Hornegger J, Choi J, Riess C, Keil A, Fahrig R (2013) CONRAD: a software framework for cone-beam imaging in radiology. Med Phys 40(11):111914CrossRefGoogle Scholar
  34. 34.
    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600CrossRefGoogle Scholar

Copyright information

© CARS 2018

Authors and Affiliations

  1. 1.Pattern Recognition LabFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Erlangen Graduate School in Advanced Optical Technologies (SAOT)Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  3. 3.Siemens Healthcare GmbHForchheimGermany

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