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Iterative weighted nuclear norm for X-ray cardiovascular angiogram image denoising

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Abstract

Low-rank regularization approximated by a nuclear norm has been proven its ability in image denoising. However, the nuclear norm is just a suboptimization of the rank norm, resulting in a big error when reducing noise. In this paper, a novel smooth and convex surrogate function, which is closer to the rank norm, is firstly proposed as a replacement of the prior nuclear norm. Then, the proposed surrogate function is approximated by its first-order Taylor expansion. Finally, a novel model called iterative weighted nuclear norm minimization scheme, solved by the single and effective alternating directions method of multipliers with a weighted singular-value thresholding operator, is formed for image denoising. Both quantitative and qualitative results obtained by applying advanced denoising methods to synthetic images will verify the effectiveness of the proposed method. Extensive application of these state-of-the-art methods to denoising of clinical X-ray cardiovascular angiograms further validates that our proposed approach performs better on reducing noise and preserving structures (especially capillaries), demonstrating that the method can yield clear X-ray angiograms with integral cardiovascular trees which are beneficial for clinicians to diagnose and analyze cardiovascular diseases.

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References

  1. Association, A.H.: Heart disease and stroke statistics-2016 update: a report from the American Heart Association. Circulation 133(4), 38–60 (2016)

    Article  Google Scholar 

  2. Wang, G.D., Sang, N., Yan, L.X., Shen, X.B.: X-ray angiogram images enhancement by facet-based adaptive anisotropic diffusion. CMIG 33, 140–147 (2009)

    Google Scholar 

  3. Zhang, T.X., Huang, Z.H., Huang, Y.N., et al.: A novel structural features-based approach to automatically extract multiple motion parameters from single-arm X-ray angiography. BSPC 32, 29–43 (2017)

    Google Scholar 

  4. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tofighi, M., Kose, K., Cetin, A.-E.: Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV). SIVP 9(S1), 41–48 (2015)

    Google Scholar 

  6. Chan, T.F., Esedoglu, S., Park, F., Yip, A.M.: Recent Developments in Total Variation Image Restoration. Mathematical Models of Computer Vision. Springer, Berlin (2005)

    Google Scholar 

  7. Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation-based image restoration. Multiscale Model. Simul. 4(2), 460–489 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Peyre, G., Bougleux, S., Cohen, L.D.: Non-local regularization of inverse problems. Inverse Probl. Imaging 5(2), 511–530 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gerig, G., Kubler, O., Kikinis, R., Jolesz, F.A.: Nonlinear anisotropic filtering of MRI data. TMI 11, 221–232 (1992)

    Google Scholar 

  10. Krissian, K., Aja-Fernandez, S.: Noise-driven anisotropic diffusion filtering of MRI. TIP 18, 2265–2274 (2009)

    MathSciNet  MATH  Google Scholar 

  11. Tarmissi, K., Hamza, A.B.: Multivariate kernel diffusion for surface denoising. SIVP 5(2), 191–201 (2011)

    Google Scholar 

  12. Swami, P.D., Jain, A.: Image denoising by supervised adaptive fusion of decomposed images restored using wave atom, curvelet and wavelet transform. SIVP 8(3), 443–459 (2014)

  13. Om, H., Biswas, M.: A generalized image denoising method using neighbouring wavelet coefficients. SIVP 9(1), 191–200 (2015)

    Google Scholar 

  14. Cui, H., Yan, G., Song, H.: A novel curvelet thresholding denoising method based on Chi-squared distribution. SIVP 9(2), 491–498 (2015)

    Google Scholar 

  15. Knaus, C., Zwicker, M.: Dual-domain image denoising. In: IEEE ICIP (2013)

  16. Knaus, C., Zwicker, M.: Progressive image denoising. TIP 23(7), 3114–3125 (2014)

    MathSciNet  Google Scholar 

  17. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. TIP 15(12), 3736–3745 (2006)

    MathSciNet  Google Scholar 

  18. Shahdoosti, H.R., Khayat, O.: Image denoising using sparse representation classification and non-subsampled shearlet transform. SIVP 10(6), 1081–1087 (2016)

    MATH  Google Scholar 

  19. Zuo, W.M., Zhang, L., Song, C.W., Zhang, D., Gao, H.J.: Gradient histogram estimation and preservation for texture enhanced image denoising. TIP 23(6), 2459–2472 (2014)

    MathSciNet  Google Scholar 

  20. Dong, W.S., Shi, G.M., Li, X.: Nonlocal image restoration with bilateral variance estimation: a low-rank approach. TIP 22(2), 700–711 (2013)

    MathSciNet  Google Scholar 

  21. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. TIP 16(8), 2080–2095 (2007)

    MathSciNet  Google Scholar 

  22. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K., et al.: BM3D image denoising with shape-adaptive principal component analysis. In: SPARS09-Signal Processing with Adaptive Sparse Structured Representations (2009)

  23. Cai, N., Zhou, Y., Wang, S., Ling, B.W.-K., Weng, S.: Image denoising via patch-based adaptive Gaussian mixture prior method. SIVP 10(6), 993–999 (2016)

    Google Scholar 

  24. Kumar, B.K.S.: Image denoising based on non-local means filter and its method noise thresholding. SIVP 7(6), 1211–1227 (2013)

    Google Scholar 

  25. Manjón, J.V., Coupé, P., Buades, A.: MRI noise estimation and denoising using non-local PCA. MIA 22, 35–47 (2015)

    Google Scholar 

  26. Xu, J., Zhang, L., Zuo, W., Zhang, D.: Patch group based nonlocal self-similarity prior learning for image denoising. In: IEEE ICCV, pp. 244-252 (2015)

  27. Van De Ville, D., Kocher, M.: Non-local means with dimensionality reduction and SURE-based parameter selection. TIP 20(9), 2683–2690 (2010)

    Google Scholar 

  28. Zhang, L., Dong, W., Zhanga, D., Shib, G.: Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recognit. 43(4), 1531–1549 (2010)

    Article  MATH  Google Scholar 

  29. Zhang, Y.Q., Ding, Y., Liu, J.Y., Guo, Z.M.: Guided image filtering using signal subspace projection. IET Image Proc. 7(3), 270–279 (2013)

    Article  MathSciNet  Google Scholar 

  30. Zhang, Y.Q., Liu, J.Y., Li, M.D., Guo, Z.M.: Joint image denoising using adaptive principal component analysis and self-similarity. Inf. Sci. 259, 128–141 (2014)

    Article  Google Scholar 

  31. Kumar, B.K.S.: Image denoising based on Gaussian/Bilateral filter and its method noise thresholding. SIVP 7(6), 1159–1172 (2013)

    Google Scholar 

  32. Dong, W.S., Li, X., Zhang, L., Shi, G.M.: Sparsity-based image denoising via dictionary learning and structural clustering. CVPR 42(7), 457–464 (2011)

    Google Scholar 

  33. Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. TPAMI 35(11), 171–184 (2013)

    Article  Google Scholar 

  34. Lu, C., Lin, Z., Yan, S.: Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization. TIP 24(2), 646–654 (2015)

    MathSciNet  Google Scholar 

  35. Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comut. Math. 9(6), 717–772 (2009)

  36. Peng, Y.G., Suo, J.L., Dai, Q.H., Xu, W.L.: From compressed sensing to low-rank matrix recovery: theory and application. Acta Autom. Sin. 39(7), 981–994 (2013)

    Article  MathSciNet  Google Scholar 

  37. Cai, J.F., Candes, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  38. Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: Fast image recovery using variable splitting and constrained optimization. TIP 19(9), 2345–2356 (2010)

  39. Gu, S., Zhang, L., Zuo, W., Feng, X.: Weighted nuclear norm minimization with application to image denoising. In: CVPR, pp. 2862–2869 (2014)

  40. Frangi, A., Niessen, W., Vincken, K., Viergever, M.: Multiscale vessel enhancement filtering. MICCAI 1496, 130–137 (1998)

    Google Scholar 

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions. We also express our sincere appreciation to Beijing Chao-yang Hospital, which provided us with the X-ray angiography image sequence to support the smooth development of our scientific research. This work is supported by the research subject of “digital subtraction angiography intelligent analysis and 3D reconstruction” in the key scientific problems research projects under the important clinical and medical information of National Basic Research Program of China (973 Program) and the Key Project of the National Natural Science Foundation of China under Grant Nos. 403040301, 61671337, 61433007 and 61227007.

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Authors and Affiliations

  1. Huazhong University of Science and Technology (HUST), Wuhan, 430074, Hubei, China

    Zhenghua Huang, Tianxu Zhang & Nong Sang

  2. Wuhan Institute of Technology, Wuhan, 430074, Hubei, China

    Zhenghua Huang & Qian Li

  3. Wuhan Donghu University, Wuhan, 430074, Hubei, China

    Hao Fang

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  1. Zhenghua Huang
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  2. Qian Li
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  3. Hao Fang
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  4. Tianxu Zhang
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  5. Nong Sang
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Correspondence to Zhenghua Huang.

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Huang, Z., Li, Q., Fang, H. et al. Iterative weighted nuclear norm for X-ray cardiovascular angiogram image denoising. SIViP 11, 1445–1452 (2017). https://doi.org/10.1007/s11760-017-1105-8

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  • DOI: https://doi.org/10.1007/s11760-017-1105-8

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