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Published in: International Journal of Computer Assisted Radiology and Surgery 1/2019

22-08-2018 | Original Article

Traditional machine learning for limited angle tomography

Authors: Yixing Huang, Yanye Lu, Oliver Taubmann, Guenter Lauritsch, Andreas Maier

Published in: International Journal of Computer Assisted Radiology and Surgery | Issue 1/2019

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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.

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Literature
1.
go back to reference Quinto ET (2006) An introduction to X-ray tomography and Radon transforms. Proc Symp APPl Math 63:1CrossRef Quinto ET (2006) An introduction to X-ray tomography and Radon transforms. Proc Symp APPl Math 63:1CrossRef
2.
go back to reference Quinto ET (2007) Local algorithms in exterior tomography. J Comput Appl Math 199(1):141CrossRef Quinto ET (2007) Local algorithms in exterior tomography. J Comput Appl Math 199(1):141CrossRef
3.
go back to reference Grünbaum FA (1980) A study of Fourier space methods for limited angle image reconstruction. Numer Funct Anal Optim 2(1):31CrossRef Grünbaum FA (1980) A study of Fourier space methods for limited angle image reconstruction. Numer Funct Anal Optim 2(1):31CrossRef
4.
go back to reference Defrise M, De Mol C (1983) A regularized iterative algorithm for limited-angle inverse Radon transform. Opt Acta: Int J Opt 30(4):403CrossRef Defrise M, De Mol C (1983) A regularized iterative algorithm for limited-angle inverse Radon transform. Opt Acta: Int J Opt 30(4):403CrossRef
5.
go back to reference Qu GR, Lan YS, Jiang M (2008) An iterative algorithm for angle-limited three-dimensional image reconstruction. Acta Math Appl Sin 24(1):157CrossRef Qu GR, Lan YS, Jiang M (2008) An iterative algorithm for angle-limited three-dimensional image reconstruction. Acta Math Appl Sin 24(1):157CrossRef
6.
go back to reference Qu GR, Jiang M (2009) Landweber iterative methods for angle-limited image reconstruction. Acta Math Appl Sin 25(2):327CrossRef Qu GR, Jiang M (2009) Landweber iterative methods for angle-limited image reconstruction. Acta Math Appl Sin 25(2):327CrossRef
7.
go back to reference 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 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.
go back to reference Louis AK, Törnig W (1980) Picture reconstruction from projections in restricted range. Math Methods Appl Sci 2(2):209CrossRef Louis AK, Törnig W (1980) Picture reconstruction from projections in restricted range. Math Methods Appl Sci 2(2):209CrossRef
9.
go back to reference Willsky AS, Prince JL (1990) Constrained sinogram restoration for limited-angle tomography. Opt Eng 29(5):535CrossRef Willsky AS, Prince JL (1990) Constrained sinogram restoration for limited-angle tomography. Opt Eng 29(5):535CrossRef
10.
go back to reference 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):035015CrossRef 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):035015CrossRef
11.
go back to reference Davison ME (1983) The ill-conditioned nature of the limited angle tomography problem. SIAM J Appl Math 43(2):428CrossRef Davison ME (1983) The ill-conditioned nature of the limited angle tomography problem. SIAM J Appl Math 43(2):428CrossRef
12.
go back to reference Louis AK (1986) Incomplete data problems in X-ray computerized tomography: I. Singular value decomposition of the limited angle transform. Numer Math 48(3):251CrossRef Louis AK (1986) Incomplete data problems in X-ray computerized tomography: I. Singular value decomposition of the limited angle transform. Numer Math 48(3):251CrossRef
13.
go back to reference Sidky EY, Pan X (2008) Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53(17):4777CrossRefPubMedPubMedCentral Sidky EY, Pan X (2008) Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53(17):4777CrossRefPubMedPubMedCentral
14.
go back to reference 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):1545CrossRefPubMed 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):1545CrossRefPubMed
15.
go back to reference Frikel J (2013) Sparse regularization in limited angle tomography. Appl Comput Harmon Anal 34(1):117CrossRef Frikel J (2013) Sparse regularization in limited angle tomography. Appl Comput Harmon Anal 34(1):117CrossRef
16.
go back to reference 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):2119CrossRefPubMed 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):2119CrossRefPubMed
17.
go back to reference 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):2742CrossRef 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):2742CrossRef
18.
go back to reference 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):307CrossRef 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):307CrossRef
19.
20.
go back to reference Zhu B, Liu JZ, Cauley SF, Rosen BR, Rosen MS (2018) Image reconstruction by domain-transform manifold learning. Nature 555(7697):487CrossRefPubMed Zhu B, Liu JZ, Cauley SF, Rosen BR, Rosen MS (2018) Image reconstruction by domain-transform manifold learning. Nature 555(7697):487CrossRefPubMed
21.
go back to reference 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 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.
go back to reference 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 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.
go back to reference Hammernik K, Würfl T, Pock T, Maier A (2017) A deep learning architecture for limited-angle computed tomography reconstruction. Procs BVM pp 92–97 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.
go back to reference Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. Procs MICCAI pp 234–241 Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. Procs MICCAI pp 234–241
25.
go back to reference Gu J, Ye JC (2017) Multi-scale wavelet domain residual learning for limited-angle CT reconstruction. Procs Fully 3D:443–447 Gu J, Ye JC (2017) Multi-scale wavelet domain residual learning for limited-angle CT reconstruction. Procs Fully 3D:443–447
26.
go back to reference Zeiler MD, Fergus R (2014) Visualizing and understanding convolutional networks. Eur Conf Comput Vis pp 818–833 Zeiler MD, Fergus R (2014) Visualizing and understanding convolutional networks. Eur Conf Comput Vis pp 818–833
27.
go back to reference Rosenblatt F (1958) The perceptron: a probabilistic model for information-storage and organization in the brain. Psychol Rev 65:386CrossRefPubMed Rosenblatt F (1958) The perceptron: a probabilistic model for information-storage and organization in the brain. Psychol Rev 65:386CrossRefPubMed
28.
29.
go back to reference Loh WY (2011) Classification and regression trees. Wiley Interdiscip Rev Data Min Knowl Discov 1(1):14CrossRef Loh WY (2011) Classification and regression trees. Wiley Interdiscip Rev Data Min Knowl Discov 1(1):14CrossRef
30.
go back to reference Quinlan JR (1987) Simplifying decision trees. Int J Man Mach Stud 27(3):221CrossRef Quinlan JR (1987) Simplifying decision trees. Int J Man Mach Stud 27(3):221CrossRef
31.
go back to reference 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) 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.
go back to reference Frank E, Hall MA, Witten IH (2016) The WEKA workbench. Online appendix for data mining: practical machine learning tools and techniques (Morgan Kaufmann, 2016) 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.
go back to reference 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):111914CrossRefPubMedPubMedCentral 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):111914CrossRefPubMedPubMedCentral
34.
go back to reference Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600CrossRefPubMed Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600CrossRefPubMed
Metadata
Title
Traditional machine learning for limited angle tomography
Authors
Yixing Huang
Yanye Lu
Oliver Taubmann
Guenter Lauritsch
Andreas Maier
Publication date
22-08-2018
Publisher
Springer International Publishing
Published in
International Journal of Computer Assisted Radiology and Surgery / Issue 1/2019
Print ISSN: 1861-6410
Electronic ISSN: 1861-6429
DOI
https://doi.org/10.1007/s11548-018-1851-2

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