Skip to main content

Advertisement

Log in

Traditional machine learning for limited angle tomography

  • Original Article
  • Published:
International Journal of Computer Assisted Radiology and Surgery Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Quinto ET (2006) An introduction to X-ray tomography and Radon transforms. Proc Symp APPl Math 63:1

    Article  Google Scholar 

  2. Quinto ET (2007) Local algorithms in exterior tomography. J Comput Appl Math 199(1):141

    Article  Google Scholar 

  3. Grünbaum FA (1980) A study of Fourier space methods for limited angle image reconstruction. Numer Funct Anal Optim 2(1):31

    Article  Google Scholar 

  4. Defrise M, De Mol C (1983) A regularized iterative algorithm for limited-angle inverse Radon transform. Opt Acta: Int J Opt 30(4):403

    Article  Google Scholar 

  5. Qu GR, Lan YS, Jiang M (2008) An iterative algorithm for angle-limited three-dimensional image reconstruction. Acta Math Appl Sin 24(1):157

    Article  Google Scholar 

  6. Qu GR, Jiang M (2009) Landweber iterative methods for angle-limited image reconstruction. Acta Math Appl Sin 25(2):327

    Article  Google Scholar 

  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 189–192

  8. Louis AK, Törnig W (1980) Picture reconstruction from projections in restricted range. Math Methods Appl Sci 2(2):209

    Article  Google Scholar 

  9. Willsky AS, Prince JL (1990) Constrained sinogram restoration for limited-angle tomography. Opt Eng 29(5):535

    Article  Google Scholar 

  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):035015

    Article  Google Scholar 

  11. Davison ME (1983) The ill-conditioned nature of the limited angle tomography problem. SIAM J Appl Math 43(2):428

    Article  Google Scholar 

  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):251

    Article  Google Scholar 

  13. Sidky EY, Pan X (2008) Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53(17):4777

    Article  PubMed  PubMed Central  Google Scholar 

  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):1545

    Article  PubMed  Google Scholar 

  15. Frikel J (2013) Sparse regularization in limited angle tomography. Appl Comput Harmon Anal 34(1):117

    Article  Google Scholar 

  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):2119

    Article  PubMed  Google Scholar 

  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):2742

    Article  Google Scholar 

  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):307

    Article  Google Scholar 

  19. Wang G (2016) A perspective on deep imaging. IEEE Access 4:8914

    Article  Google Scholar 

  20. Zhu B, Liu JZ, Cauley SF, Rosen BR, Rosen MS (2018) Image reconstruction by domain-transform manifold learning. Nature 555(7697):487

    Article  CAS  PubMed  Google Scholar 

  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 37

  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: 341–344

  23. Hammernik K, Würfl T, Pock T, Maier A (2017) A deep learning architecture for limited-angle computed tomography reconstruction. Procs BVM pp 92–97

  24. Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. Procs MICCAI pp 234–241

  25. Gu J, Ye JC (2017) Multi-scale wavelet domain residual learning for limited-angle CT reconstruction. Procs Fully 3D:443–447

    Google Scholar 

  26. Zeiler MD, Fergus R (2014) Visualizing and understanding convolutional networks. Eur Conf Comput Vis pp 818–833

  27. Rosenblatt F (1958) The perceptron: a probabilistic model for information-storage and organization in the brain. Psychol Rev 65:386

    Article  CAS  PubMed  Google Scholar 

  28. Kohonen T (1988) An introduction to neural computing. Neural Netw 1(1):3

    Article  Google Scholar 

  29. Loh WY (2011) Classification and regression trees. Wiley Interdiscip Rev Data Min Knowl Discov 1(1):14

    Article  Google Scholar 

  30. Quinlan JR (1987) Simplifying decision trees. Int J Man Mach Stud 27(3):221

    Article  Google Scholar 

  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)

  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)

  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):111914

    Article  PubMed  PubMed Central  Google Scholar 

  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):600

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Yixing Huang or Yanye Lu.

Ethics declarations

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, Y., Lu, Y., Taubmann, O. et al. Traditional machine learning for limited angle tomography. Int J CARS 14, 11–19 (2019). https://doi.org/10.1007/s11548-018-1851-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11548-018-1851-2

Keywords

Navigation