Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter April 10, 2018

An adaptive iteration reconstruction method for limited-angle CT image reconstruction

  • Chengxiang Wang , Li Zeng EMAIL logo , Lingli Zhang , Yumeng Guo and Wei Yu

Abstract

The limited-angle computed tomography (CT) reconstruction problem is an ill-posed inverse problem, and the parameter selection for limited-angle CT iteration reconstruction is a difficult issue in practical application. In this paper, to alleviate the instability of limited-angle CT reconstruction problem and automatize the reconstruction process, we propose an adaptive iteration reconstruction method that the regularization parameter is chosen adaptively via the plot of the normalized wavelet coefficients fitting residual versus that the 0 regularization part. The experimental results show that the reconstructed images using the method with adapted regularization parameter are almost as good as that using the non-adapted parameter method in terms of visual inspection, in addition, our method has an advantage in adaptively choosing the regularization parameter.

Award Identifier / Grant number: 61701174

Award Identifier / Grant number: 61771003

Funding statement: This work is supported by the National Natural Science Foundation of China (No.61771003 and No.61701174), the National Instrumentation Program of China (No. 2013YQ030629), the Hubei Provincial Natural Science Foundation of China (No. 2017CFB168), the Education Department of Hubei Province Science and Technology Research Project (No. Q20172803), and the PhD Start-up Fund of HBUST (No. BK1527).

References

[1] K. Bredies, K. Kunisch and T. Pock, Total generalized variation, SIAM J. Imaging Sci. 3 (2010), no. 3, 492–526. 10.1137/090769521Search in Google Scholar

[2] M. K. Cho, H. K. Kim, H. Youn and S. S. Kim, A feasibility study of digital tomosynthesis for volumetric dental imaging, J. Instrum. 7 (2012), no. 3, Article ID P03007. 10.1088/1748-0221/7/03/P03007Search in Google Scholar

[3] C. Clason, B. Jin and K. Kunisch, A semismooth Newton method for L1 data fitting with automatic choice of regularization parameters and noise calibration, SIAM J. Imaging Sci. 3 (2010), no. 2, 199–231. 10.1137/090758003Search in Google Scholar

[4] I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. 57 (2004), no. 11, 1413–1457. 10.1002/cpa.20042Search in Google Scholar

[5] M. E. Davison, The ill-conditioned nature of the limited angle tomography problem, SIAM J. Appl. Math. 43 (1983), no. 2, 428–448. 10.1137/0143028Search in Google Scholar

[6] B. Dong and Y. Zhang, An efficient algorithm for 0 minimization in wavelet frame based image restoration, J. Sci. Comput. 54 (2013), no. 2–3, 350–368. 10.1007/s10915-012-9597-4Search in Google Scholar

[7] J. M. Fadili and G. Peyré, Total variation projection with first order schemes, IEEE Trans. Image Process. 20 (2011), no. 3, 657–669. 10.1109/TIP.2010.2072512Search in Google Scholar PubMed

[8] J. Frikel, Reconstructions in limited angle x-ray tomography: Characterization of classical reconstructions and adapted curvelet sparse regularization, Ph.D. thesis, Technische Universität München, 2013. Search in Google Scholar

[9] J. Frikel, Sparse regularization in limited angle tomography, Appl. Comput. Harmon. Anal. 34 (2013), no. 1, 117–141. 10.1016/j.acha.2012.03.005Search in Google Scholar

[10] J. Frikel and E. T. Quinto, Characterization and reduction of artifacts in limited angle tomography, Inverse Problems 29 (2013), no. 12, Article ID 125007. 10.1088/0266-5611/29/12/125007Search in Google Scholar

[11] H. Gao, J. F. Cai, Z. W. Shen and H. Zhao, GPU-based iterative cone-beam CT reconstruction using tight frame regularization, Phys. Med. Biol. 56 (2011), no. 13, 3781–3798. Search in Google Scholar

[12] H. Gao, L. Zhang, Z. Chen, Y. Xing, J. Cheng and Z. Qi, Direct filtered-backprojection-type reconstruction from a straight-line trajectory, Optical Eng. 46 (2007), no. 5, 1–11. 10.1117/1.2739624Search in Google Scholar

[13] K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki and S. Siltanen, Sparse tomography, SIAM J. Sci. Comput. 35 (2013), no. 3, B644–B665. 10.1137/120876277Search in Google Scholar

[14] P. C. Hansen and D. P. O’Leary, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993), no. 6, 1487–1503. 10.1137/0914086Search in Google Scholar

[15] G. T. Herman, Fundamentals of Computerized Tomography. Image Reconstruction from Projections, 2nd ed., Adv. Pattern Recognit, Springer, Dordrecht, 2009. 10.1007/978-1-84628-723-7Search in Google Scholar

[16] G. T. Herman and R. Davidi, Image reconstruction from a small number of projections, Inverse Problems 24 (2008), no. 4, Article ID 045011. 10.1088/0266-5611/24/4/045011Search in Google Scholar PubMed PubMed Central

[17] Z. Hou, Permanence, global attraction and stability, Lotka–Volterra and Related Systems, De Gruyter Ser. Math. Life Sci. 2, De Gruyter, Berlin (2013), 1–62. 10.1515/9783110269840.1Search in Google Scholar

[18] M. Jansen, Generalized cross validation in variable selection with and without shrinkage, J. Statist. Plann. Inference 159 (2015), 90–104. 10.1016/j.jspi.2014.10.007Search in Google Scholar

[19] M. Jiang and G. Wang, Convergence of the simultaneous algebraic reconstruction technique (SART), IEEE Trans. Image Process. 12 (2003), no. 8, 957–961. 10.1109/TIP.2003.815295Search in Google Scholar PubMed

[20] V. Kolehmainen, S. Siltanen, S. Järvenpää, J. P. Kaipio, P. Koistinen, M. Lassas, J. Pirttila and E. Somersalo, Statistical inversion for medical x-ray tomography with few radiographs: II. Application to dental radiology, Phys. Med. Biol. 48 (2003), 1465–1490. 10.1088/0031-9155/48/10/315Search in Google Scholar PubMed

[21] H. Kudo, F. Noo, M. Defrise and R. Clackdoyle, New super-short-scan algorithms for fan-beam and cone-beam reconstruction, Nuclear Science Symposium Conference Record, IEEE Press, Piscataway (2002), 902–906. 10.1109/NSSMIC.2002.1239470Search in Google Scholar

[22] H. Li, X. Chen, Y. Wang, Z. Zhou, Q. Zhu and D. Yu, Sparse CT reconstruction based on multi-direction anisotropic total variation (MDATV), Biomed. Eng. 13 (2014), no. 1, 1–27. 10.1186/1475-925X-13-92Search in Google Scholar PubMed PubMed Central

[23] Y. Liu, J. Ma, Y. Fan and Z. Liang, Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction, Phys. Med. Biol. 57 (2012), no. 23, 7923–7956. 10.1088/0031-9155/57/23/7923Search in Google Scholar PubMed PubMed Central

[24] Y. S. Liu, Z. F. Zhan, J. F. Cai, D. Guo, Z. Chen and X. B. Qu, Projected iterative soft-thresholding algorithm for tight frames in compressed sensing in magnetic resonance imaging, IEEE Trans Med. Imag. 35 (2016), no. 9, 2130–2140. 10.1109/TMI.2016.2550080Search in Google Scholar PubMed

[25] X. Mou, J. Wu, T. Bai, Q. Xu, H. Y. Yu and G. Wang, Dictionary learning based low-dose x-ray CT reconstruction using a balancing principle, Proc. SPIE 9212 (2014), 10.1117/12.2065459. 10.1117/12.2065459Search in Google Scholar

[26] J. L. Mueller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, Comput. Sci. Eng. 10, Society for Industrial and Applied Mathematics, Philadelphia, 2012. 10.1137/1.9781611972344Search in Google Scholar

[27] F. Natterer, The Mathematics of Computerized Tomography, Class. Appl. Math. 32, Society for Industrial and Applied Mathematics, Philadelphia, 2001. 10.1137/1.9780898719284Search in Google Scholar

[28] F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction, SIAM Monogr. Math. Model. Comp., Society for Industrial and Applied Mathematics, Philadelphia, 2001. 10.1137/1.9780898718324Search in Google Scholar

[29] L. V. Nguyen, How strong are streak artifacts in limited angle computed tomography?, Inverse Problems 31 (2015), no. 5, Article ID 055003. 10.1088/0266-5611/31/5/055003Search in Google Scholar

[30] S. Niu, Y. Gao, Z. Bian, J. Huang, W. Chen, G. Yu and J. Ma, Sparse-view x-ray CT reconstruction via total generalized variation regularization, Phys. Med. Biol. 59 (2014), no. 12, 2997–3017. 10.1088/0031-9155/59/12/2997Search in Google Scholar PubMed PubMed Central

[31] F. Noo, M. Defrise, R. Clackdoyle and H. Kudo, Image reconstruction from fan-beam projections on less than a short scan, Phys. Med. Biol. 47 (2002), no. 14, 2525–2546. 10.1088/0031-9155/47/14/311Search in Google Scholar PubMed

[32] F. Noo and D. J. Heuscher, Image reconstruction from cone-beam data on a circular short-scan, Proc. SPIE 4684 (2002), 10.1117/12.467199. 10.1117/12.467199Search in Google Scholar

[33] M. Rantala, S. Vänskä and S. Järvenpää, Wavelet-based reconstruction for limited angle x-ray tomography, IEEE Trans. Med. Imag. 25 (2006), no. 2, 210–217. 10.1109/TMI.2005.862206Search in Google Scholar

[34] W. Ring, Structural properties of solutions to total variation regularization problems, ESAIM Math. Model. Numer. Anal. 34 (2000), no. 4, 799–810. 10.1051/m2an:2000104Search in Google Scholar

[35] W. P. Segars, D. S. Lalush and B. M. W. Tsui, A realistic splinebased dynamic heart phantom, IEEE Trans. Nucl. Sci. 46 (1999), 503–506. 10.1109/23.775570Search in Google Scholar

[36] M. M. Seger and P. E. Danielsson, Scanning of logs with linear cone-beam tomography, Comp. Electron. Agriculture 41 (2003), 45–62. 10.1016/S0168-1699(03)00041-3Search in Google Scholar

[37] E. Y. Sidky and X. C. Pan, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Phys. Med. Biol. 53 (2008), no. 17, 47–77. 10.1088/0031-9155/53/17/021Search in Google Scholar PubMed PubMed Central

[38] M. Storath, A. Weinmann, J. Frikel and M. Unser, Joint image reconstruction and segmentation using the Potts model, Inverse Problems 31 (2015), no. 2, Article ID 025003. 10.1088/0266-5611/31/2/025003Search in Google Scholar

[39] Y. L. Sun and J. X. Tao, Image reconstruction from few views by0-norm optimization, Chinese Phys. B 23 (2014), no. 7, 762–766. Search in Google Scholar

[40] Z. Wang, A. C. Bovik, H. R. Sheikh and E. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Trans Image Process. 13 (2004), 600–612. 10.1109/TIP.2003.819861Search in Google Scholar PubMed

[41] M. Wieczorek, J. Frikel, J. Vogel, E. Eggl, F. Kopp, P. B. Noël and T. Lasser, X-ray computed tomography using curvelet sparse regularization, Med. Phys. 42 (2015), no. 4, 1555–1565. 10.1118/1.4914368Search in Google Scholar PubMed

[42] J. Xie and J. Zou, An improved model function method for choosing regularization parameters in linear inverse problems, Inverse Problems 18 (2002), no. 3, 631–643. 10.1088/0266-5611/18/3/307Search in Google Scholar

[43] Q. Xu, H. Y. Yu, X. Mou, L. Zhang, J. Hsieh and G. Wang, Low-dose X-ray CT reconstruction via dictionary learning, IEEE Trans. Med. Imag. 31 (2012), no. 9, 1682–1697. 10.1109/TMI.2012.2195669Search in Google Scholar PubMed PubMed Central

[44] Y. Zhang, B. Dong and Z. Lu, 0 minimization for wavelet frame based image restoration, Math. Comp. 82 (2013), no. 282, 995–1015. 10.1090/S0025-5718-2012-02631-7Search in Google Scholar

[45] Y. Zhang, Y. Wang, W. Zhang, F. Lin, Y. Pu and J. Zhou, Statistical iterative reconstruction using adaptive fractional order regularization, Biomed. Opt. Express 7 (2016), no. 3, 1015–1029. 10.1364/BOE.7.001015Search in Google Scholar PubMed PubMed Central

[46] B. Zhao, H. Gao, H. Ding and S. Molloi, Tight-frame based iterative image reconstruction for spectral breast CT, Med. Phys. 40 (2013), no. 3, Article ID 031905. 10.1118/1.4790468Search in Google Scholar PubMed PubMed Central

Received: 2017-04-06
Revised: 2017-10-22
Accepted: 2018-03-13
Published Online: 2018-04-10
Published in Print: 2018-12-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 25.4.2024 from https://www.degruyter.com/document/doi/10.1515/jiip-2017-0034/html
Scroll to top button