Cluster Sparsity Field: An Internal Hyperspectral Imagery Prior for Reconstruction

  • Lei Zhang
  • Wei Wei
  • Yanning Zhang
  • Chunhua Shen
  • Anton van den Hengel
  • Qinfeng Shi
Article
  • 97 Downloads

Abstract

Hyperspectral images (HSIs) have significant advantages over more traditional image types for a variety of computer vision applications dues to the extra information available. The practical reality of capturing and transmitting HSIs however, means that they often exhibit large amounts of noise, or are undersampled to reduce the data volume. Methods for combating such image corruption are thus critical to many HSIs applications. Here we devise a novel cluster sparsity field (CSF) based HSI reconstruction framework which explicitly models both the intrinsic correlation between measurements within the spectrum for a particular pixel, and the similarity between pixels due to the spatial structure of the HSI. These two priors have been shown to be effective previously, but have been always considered separately. By dividing pixels of the HSI into a group of spatial clusters on the basis of spectrum characteristics, we define CSF, a Markov random field based prior. In CSF, a structured sparsity potential models the correlation between measurements within each spectrum, and a graph structure potential models the similarity between pixels in each spatial cluster. Then, we integrate the CSF prior learning and image reconstruction into a unified variational framework for optimization, which makes the CSF prior image-specific, and robust to noise. It also results in more accurate image reconstruction compared with existing HSI reconstruction methods, thus combating the effects of noise corruption or undersampling. Extensive experiments on HSI denoising and HSI compressive sensing demonstrate the effectiveness of the proposed method.

Keywords

Structured sparsity Spatial similarity Hyperspectral denoising Compressive sensing 

Notes

Acknowledgements

This work is supported in part by the National Natural Science Foundation of China (Nos. 61671385, 61231016, 61571354), Natural Science Basis Research Plan in Shaanxi Province of China (No. 2017JM6021), Innovation Foundation for Doctoral Dissertation of Northwestern Polytechnical University (No. CX201521) and Australian Research Council Grant (No. FT120100969). Lei Zhang’s contribution was made when he was a visiting student at the University of Adelaide.

References

  1. Aharon, M., Elad, M., & Bruckstein, A. (2006). K-svd: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11), 4311–4322.CrossRefMATHGoogle Scholar
  2. Akbari, H., Kosugi, Y., Kojima, K., & Tanaka, N. (2010). Detection and analysis of the intestinal ischemia using visible and invisible hyperspectral imaging. IEEE Transactions on Biomedical Engineering, 57(8), 2011–2017.CrossRefGoogle Scholar
  3. August, Y., & Stern, A. (2013). Compressive sensing spectrometry based on liquid crystal devices. Optics Letters, 38(23), 4996–4999.CrossRefGoogle Scholar
  4. August, Y., Vachman, C., Rivenson, Y., & Stern, A. (2013). Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains. Applied optics, 52(10), D46–D54.CrossRefGoogle Scholar
  5. Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends\({\textregistered }\). Machine Learning, 3(1), 1–122.Google Scholar
  6. Buades, A., Coll, B., Morel, J. M. (2005). A non-local algorithm for image denoising. In IEEE computer society conference on computer vision and pattern recognition, 2005. CVPR 2005 (Vol. 2, pp. 60–65). IEEE.Google Scholar
  7. Chen, C., Huang, J. (2012). Compressive sensing mri with wavelet tree sparsity. In Advances in Neural Information Processing Systems, pp. 1115–1123Google Scholar
  8. Chen, F., Zhang, L., Yu, H. (2015). External patch prior guided internal clustering for image denoising. In Proceedings of the IEEE international conference on computer vision (pp. 603–611).Google Scholar
  9. Cotter, S. F., Rao, B. D., Engan, K., & Kreutz-Delgado, K. (2005). Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Transactions on Signal Processing, 53(7), 2477–2488.MathSciNetCrossRefMATHGoogle Scholar
  10. Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Transactions on Image Processing, 16(8), 2080–2095.MathSciNetCrossRefGoogle Scholar
  11. Dong, W., Zhang, D., Shi, G. (2011). Centralized sparse representation for image restoration. In: 2011 IEEE international conference on computer vision (ICCV) (pp 1259–1266). IEEE.Google Scholar
  12. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al. (2004). Least angle regression. The Annals of statistics, 32(2), 407–499.MathSciNetCrossRefMATHGoogle Scholar
  13. Elhamifar, E., & Vidal, R. (2013). Sparse subspace clustering: Algorithm, theory, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(11), 2765–2781.CrossRefGoogle Scholar
  14. Foster, D. H., Amano, K., Nascimento, S., & Foster, M. J. (2006). Frequency of metamerism in natural scenes. JOSA A, 23(10), 2359–2372.CrossRefGoogle Scholar
  15. Fu, Y., Lam, A., Sato, I., & Sato, Y. (2017). Adaptive spatial-spectral dictionary learning for hyperspectral image restoration. International Journal of Computer Vision, 122(2), 228–245.MathSciNetCrossRefGoogle Scholar
  16. Greer, J. B. (2012). Sparse demixing of hyperspectral images. IEEE Transactions on Image Processing, 21(1), 219–228.MathSciNetCrossRefMATHGoogle Scholar
  17. Huang, J., Zhang, T., & Metaxas, D. (2011). Learning with structured sparsity. The Journal of Machine Learning Research, 12, 3371–3412.MathSciNetMATHGoogle Scholar
  18. Ji, S., Xue, Y., & Carin, L. (2008). Bayesian compressive sensing. IEEE Transactions on Signal Processing, 56(6), 2346–2356.MathSciNetCrossRefGoogle Scholar
  19. Kerekes, J. P., & Baum, J. E. (2005). Full-spectrum spectral imaging system analytical model. IEEE Transactions on Geoscience and Remote Sensing, 43(3), 571–580.CrossRefGoogle Scholar
  20. Li, B., Zhang, Y., Lin, Z., Lu, H. (2015). Center CMI (2015) Subspace clustering by mixture of gaussian regression. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 2094–2102).Google Scholar
  21. Lin, D., Fisher, J. (2012). Manifold guided composite of markov random fields for image modeling. In 2012 IEEE conference on computer vision and pattern recognition (CVPR) (pp. 2176–2183). IEEE.Google Scholar
  22. Liu, L., Wang, P., Shen, C., Wang, L., Van Den Hengel, A., Wang, C., et al. (2017). Compositional model based fisher vector coding for image classification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 99, 1–1.Google Scholar
  23. Liu, X., Bourennane, S., & Fossati, C. (2012). Denoising of hyperspectral images using the parafac model and statistical performance analysis. IEEE Transactions on Geoscience and Remote Sensing, 50(10), 3717–3724.CrossRefGoogle Scholar
  24. Lu, C. Y., Min, H., Zhao, Z. Q., Zhu, L., Huang, D. S., Yan, S. (2012). Robust and efficient subspace segmentation via least squares regression. In Computer vision–ECCV 2012 (pp 347–360). Springer.Google Scholar
  25. Maggioni, M., Boracchi, G., Foi, A., & Egiazarian, K. (2012). Video denoising, deblocking, and enhancement through separable 4-d nonlocal spatiotemporal transforms. IEEE Transactions on Image Processing, 21(9), 3952–3966.MathSciNetCrossRefMATHGoogle Scholar
  26. Maggioni, M., Katkovnik, V., Egiazarian, K., & Foi, A. (2013). Nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE Transactions on Image Processing, 22(1), 119–133.MathSciNetCrossRefMATHGoogle Scholar
  27. Martin, G., Bioucas-Dias, J. M., & Plaza, A. (2015). Hyca: A new technique for hyperspectral compressive sensing. IEEE Transactions on Geoscience and Remote Sensing, 53(5), 2819–2831.CrossRefGoogle Scholar
  28. Nasrabadi, N. M. (2014). Hyperspectral target detection: An overview of current and future challenges. IEEE Signal Processing Magazine, 31(1), 34–44.CrossRefGoogle Scholar
  29. Peng, Y., Meng, D., Xu, Z., Gao, C., Yang, Y., Zhang, B. (2014). Decomposable nonlocal tensor dictionary learning for multispectral image denoising. In 2014 IEEE conference on computer vision and pattern recognition (CVPR) (pp. 2949–2956). IEEE.Google Scholar
  30. Qian, Y., & Ye, M. (2013). Hyperspectral imagery restoration using nonlocal spectral-spatial structured sparse representation with noise estimation. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 6(2), 499–515.CrossRefGoogle Scholar
  31. Qian, Y., Shen, Y., Ye, M., Wang, Q. (2012). 3-d nonlocal means filter with noise estimation for hyperspectral imagery denoising. In 2012 IEEE international geoscience and remote sensing symposium (IGARSS) (pp. 1345–1348). IEEE.Google Scholar
  32. Rasti, B., Sveinsson, J. R., Ulfarsson, M. O., Benediktsson, J. A. (2013). Hyperspectral image denoising using a new linear model and sparse regularization. In 2013 IEEE international geoscience and remote sensing symposium (IGARSS) (pp. 457–460). IEEE.Google Scholar
  33. Renard, N., Bourennane, S., & Blanc-Talon, J. (2008). Denoising and dimensionality reduction using multilinear tools for hyperspectral images. IEEE Geoscience and Remote Sensing Letters, 5(2), 138–142.CrossRefGoogle Scholar
  34. Schmidt, U., Roth, S. (2014). Shrinkage fields for effective image restoration. In 2014 IEEE conference on computer vision and pattern recognition (CVPR) (pp. 2774–2781). IEEE.Google Scholar
  35. Tropp, J. A., & Gilbert, A. C. (2007). Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 53(12), 4655–4666.MathSciNetCrossRefMATHGoogle Scholar
  36. Van Nguyen, H., Banerjee, A., Chellappa, R. (2010). Tracking via object reflectance using a hyperspectral video camera. In 2010 IEEE computer society conference on computer vision and pattern recognition workshops (CVPRW) (pp. 44–51). IEEE.Google Scholar
  37. Wang, J. (2012). Locally linear embedding. Berlin Heidelberg: Springer.CrossRefGoogle Scholar
  38. Wang, P., Cao, Y., Shen, C., Liu, L., & Shen, H. T. (2017). Temporal pyramid pooling based convolutional neural network for action recognition. IEEE Transactions on Circuits and Systems for Video Technology, 27(12), 2613–2622.CrossRefGoogle Scholar
  39. Wang, P., Liu, L., Shen, C., Huang, Z., Van Den Hengel, A., Shen, HT. (2016). Whats wrong with that object? identifying images of unusual objects by modelling the detection score distribution. In Computer vision and pattern recognition (pp. 1573–1581)Google Scholar
  40. Wang, Z., Nasrabadi, N. M., & Huang, T. S. (2015). Semisupervised hyperspectral classification using task-driven dictionary learning with laplacian regularization. IEEE Transactions on Geoscience and Remote Sensing, 53(3), 1161–1173.CrossRefGoogle Scholar
  41. Wei, W., Zhang, L., Tian, C., Plaza, A., & Zhang, Y. (2017). Structured sparse coding-based hyperspectral imagery denoising with intracluster filtering. IEEE Transactions on Geoscience and Remote Sensing, 55(12), 6860–6876.CrossRefGoogle Scholar
  42. Wipf, D. P., Rao, B. D., & Nagarajan, S. (2011). Latent variable bayesian models for promoting sparsity. IEEE Transactions on Information Theory, 57(9), 6236–6255.MathSciNetCrossRefMATHGoogle Scholar
  43. Yasuma, F., Mitsunaga, T., Iso, D., & Nayar, S. K. (2010). Generalized assorted pixel camera: Postcapture control of resolution, dynamic range, and spectrum. IEEE Transactions on Image Processing, 19(9), 2241–2253.MathSciNetCrossRefMATHGoogle Scholar
  44. Yuan, Q., Zhang, L., & Shen, H. (2012). Hyperspectral image denoising employing a spectral-spatial adaptive total variation model. IEEE Transactions on Geoscience and Remote Sensing, 50(10), 3660–3677.CrossRefGoogle Scholar
  45. Zhang, H., He, W., Zhang, L., Shen, H., & Yuan, Q. (2014). Hyperspectral image restoration using low-rank matrix recovery. IEEE Transactions on Geoscience and Remote Sensing, 52(8), 4729–4743.CrossRefGoogle Scholar
  46. Zhang, L., Wei, W., Shi, Q., Shen, C., Van Den Hengel, A., Zhang, Y. (2017). Beyond low rank: A data-adaptive tensor completion method arXiv:1708.01008
  47. Zhang, L., Wei, W., Tian, C., Li, F., & Zhang, Y. (2016a). Exploring structured sparsity by a reweighted laplace prior for hyperspectral compressive sensing. IEEE Transactions on Image Processing, 25(10), 4974–4988.MathSciNetCrossRefGoogle Scholar
  48. Zhang, L., Wei, W., Zhang, Y., Li, F., Shen, C., Shi, Q. (2015). Hyperspectral compressive sensing using manifold-structured sparsity prior. In Proceedings of the IEEE international conference on computer vision (ICCV) (pp. 3550–3558)Google Scholar
  49. Zhang, L., Wei, W., Zhang, Y., Shen, C., Van Den Hengel, A., Shi, Q. (2016b). Cluster sparsity field hyperspectal imagery denoising. In European conference on computer vision. Springer.Google Scholar
  50. Zhang, L., Wei, W., Zhang, Y., Shen, C., Van Den Hengel, A., & Shi, Q. (2016c). Dictionary learning for promoting structured sparsity in hyperspectral compressive sensing. IEEE Transactions on Geoscience and Remote Sensing, 54(12), 7223–7235.CrossRefGoogle Scholar
  51. Zhang, Z., & Rao, B. D. (2011). Sparse signal recovery with temporally correlated source vectors using sparse bayesian learning. IEEE Journal of Selected Topics in Signal Processing, 5(5), 912–926.CrossRefGoogle Scholar
  52. Zhao, Q., Meng, D., Xu, Z., Zuo, W., Zhang, L. (2014). Robust principal component analysis with complex noise. In ICML (pp. 55–63)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer ScienceNorthwestern Polytechnical UniversityXi’anChina
  2. 2.School of Computer ScienceThe University of AdelaideAdelaideAustralia

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