April  2020, 14(2): 339-361. doi: 10.3934/ipi.2020015

Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

1. 

Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

2. 

Department of Mathematics, Case Western Reserve University, Cleveland, OH, 44106, USA

* Corresponding author: Weihong Guo

Received  June 2019 Revised  October 2019 Published  February 2020

Hyperspectral image (HSI) super-resolution is a technique to improve the spatial resolution of a HSI for better visual perception and down stream applications. This is a very ill-posed inverse problem and is often solved by fusing the low-resolution (LR) HSI with a high-resolution (HR) multispectral image (MSI). It is more challenging for blind HSI super-resolution, i.e., when the spatial degradation operators are completely unknown. In this paper, we propose a novel sparse tensor factorization model for the task of blind HSI super-resolution using the spatial non-local self-similarity and spectral global correlation of HSIs. Image clustering method is employed to collect some similar 3D cubes of HSIs which can be formed as some 4D image clusters with high correlation. We conduct cluster wise computation to not only save computation time but also to introduce a non-local regularity originated from the redundancy of cubes. By using the sparsity of tensor decomposition and the low-rank in non-local self-similarity direction underlying 4D similar clusters, we design a sparse tensor regularization term, which preserves the spatial-spectral structural correlation of HSIs. In addition, we present a proximal alternating direction method of multipliers (ADMM) based algorithm to efficiently solve the proposed model. Numerical experiments demonstrate that the proposed model outperforms many state-of-the-art HSI super-resolution methods.

Citation: Wei Wan, Weihong Guo, Jun Liu, Haiyang Huang. Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank. Inverse Problems & Imaging, 2020, 14 (2) : 339-361. doi: 10.3934/ipi.2020015
References:
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N. Akhtar, F. Shafait and A. Mian, Bayesian sparse representation for hyperspectral image super resolution, IEEE Computer Vision and Pattern Recognition (CVPR), (2015), 3631-3640. doi: 10.1109/CVPR.2015.7298986.  Google Scholar

[2]

J. M. Bioucas-DiasA. PlazaG. Camps-VallsP. ScheundersN. Nasrabadi and J. Chanussot, Hyperspectral remote sensing data analysis and future challenges, IEEE Geoscience and Remote Sensing Magazine, 1 (2013), 6-36.  doi: 10.1109/MGRS.2013.2244672.  Google Scholar

[3]

J. M. Bioucas-Dias and A. Plaza, Hyperspectral unmixing: Geometrical, statistical, and sparse regression-based approaches, Image and Signal Processing for Remote Sensing XVI, (2010), 354-379. Google Scholar

[4]

Y. Chang, L. Yan, H. Fang, S. Zhong and Z. Zhang, Weighted Low-Rank Tensor Recovery for Hyperspectral Image Restoration, ARXIV, 2017. Google Scholar

[5]

C. F. Caiafa and A. Cichocki, Computing sparse representations of multidimensional signals using kronecker bases, Neural Computation, 25 (2013), 186-220.  doi: 10.1162/NECO_a_00385.  Google Scholar

[6]

W. DongF. FuG. ShiX. CaoJ. WuG. Li and X. Li, Hyperspectral image super-resolution via non-negative structured sparse representation, IEEE Transactions on Image Processing, 25 (2016), 2337-2352.  doi: 10.1109/TIP.2016.2542360.  Google Scholar

[7]

R. Dian, L. Fang and S. Li, Hyperspectral image super-resolution via non-local sparse tensor factorization, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017). doi: 10.1109/CVPR.2017.411.  Google Scholar

[8]

F. Dell''AcquaP. GambaA. FerrariJ. A. PalmasonJ. A. Benediktsson and K. Arnason, Exploiting spectral and spatial information in hyperspectral urban data with high resolution, IEEE Geoscience and Remote Sensing Letters, 1 (2004), 322-326.   Google Scholar

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H. FanY. ChenY. GuoH. Zhang and G. Kuang, Hyperspectral image restoration using low-rank tensor recovery, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 10 (2017), 4589-4604.  doi: 10.1109/JSTARS.2017.2714338.  Google Scholar

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C. JiaM. Shao and Y. Fu, Sparse canonical temporal alignment with deep tensor decomposition for action recognition, IEEE Transactions on Image Processing, 26 (2017), 738-750.  doi: 10.1109/TIP.2016.2621664.  Google Scholar

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C. I. KanatsoulisX. FuN. D. Sidiropoulos and W. K. Ma, Hyperspectral super-resolution: A coupled tensor factorization approach, IEEE Transactions on Signal Processing, 66 (2018), 6503-6517.  doi: 10.1109/TSP.2018.2876362.  Google Scholar

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T. G. Kolda and B. W. Bader, Tensor decompositions and applications, Siam Review, 51 (2009), 455-500.  doi: 10.1137/07070111X.  Google Scholar

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W. LiG. WuF. Zhang and Q. Du, Hyperspectral image classification using deep pixel-pair features, IEEE Transactions on Geoscience and Remote Sensing, 55 (2016), 844-853.   Google Scholar

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S. LiR. DianL. Fang and J. M. Bioucas-Dias, Fusing hyperspectral and multispectral images via coupled sparse tensor factorization, IEEE Transactions on Image Processing, 27 (2018), 4118-4130.  doi: 10.1109/TIP.2018.2836307.  Google Scholar

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M. J. Montag and H. Stephani, Hyperspectral unmixing from incomplete and noisy data, Journal of Imaging, 2 (2016), p7. doi: 10.3390/jimaging2010007.  Google Scholar

[20]

J. MaH. ZhouJ. ZhaoY. CaoJ. Jiang and J. Tian, Robust feature matching for remote sensing image registration via locally linear transforming, IEEE Transactions on Geoscience and Remote Sensing, 53 (2015), 6469-6481.  doi: 10.1109/TGRS.2015.2441954.  Google Scholar

[21]

H. V. Nguyen, A. Banerjee and R. Chellappa, Tracking via object reflectance using a hyperspectral video camera, IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Workshops, (2010). doi: 10.1109/CVPRW.2010.5543780.  Google Scholar

[22]

Y. Peng, D. Meng, Z. Xu, C. Cao, Y. Yang and B. Zhang, Decomposable nonlocal tensor dictionary learning for multispectral image denoising, IEEE Conference on Computer Vision and Pattern Recognition, (2014). doi: 10.1109/CVPR.2014.377.  Google Scholar

[23]

Y. QianF. XiongS. ZengJ. Zhou and Y. Y. Tang, Matrix-vector nonnegative tensor factorization for blind unmixing of hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 55 (2017), 1776-1792.   Google Scholar

[24]

M. SimoesJ. M. Bioucas-DiasL. B. Almeida and J. Chanussot, A convex formulation for hyperspectral image superresolution via subspace-based regularization, IEEE Transactions on Geoscience and Remote Sensing, 53 (2014), 3373-3388.  doi: 10.1109/TGRS.2014.2375320.  Google Scholar

[25]

S. SoltaniM. E. Kilmer and P. C. Hansen, A tensor-based dictionary learning approach to tomographic image reconstruction, BIT Numerical Mathematics, 56 (2016), 1425-1454.  doi: 10.1007/s10543-016-0607-z.  Google Scholar

[26]

Y. TarabalkaJ. Chanussot and J. A. Benediktsson, Segmentation and classification of hyperspectral images using minimum spanning forest grown from automatically selected markers, IEEE Transactions on Systems, Man, and Cybernetics, 40 (2010), 1267-1279.  doi: 10.1109/TSMCB.2009.2037132.  Google Scholar

[27]

X. C. Tai and C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, International Conference on Scale Space and Variational Methods in Computer Vision, (2009), 502-513. Google Scholar

[28]

M. UzairA. Mahmood and A. Mian, Hyperspectral face recognition using 3D-DCT and partial least squares, BMVC, 10 (2013), 1-57.  doi: 10.5244/C.27.57.  Google Scholar

[29]

M. UzairA. Mahmood and A. Mian, Hyperspectral face recognition with spatiospectral information fusion and PLS regression, IEEE Transactions on Image Processing, 24 (2015), 1127-1137.  doi: 10.1109/TIP.2015.2393057.  Google Scholar

[30]

G. VaneR. O. GreenT. G. ChrienH. T. EnmarkE. G. Hansen and W. M. Porter, The airborne visible/infrared imaging spectrometer (AVIRIS), Remote Sensing of Environment, 44 (1993), 127-143.  doi: 10.1016/0034-4257(93)90012-M.  Google Scholar

[31]

E. Wycoff, T. H. Chan, K. Jia, W. K. Ma and Y. Ma, A non-negative sparse promoting algorithm for high resolution hyperspectral imaging, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (2013), 1409-1413. doi: 10.1109/ICASSP.2013.6637883.  Google Scholar

[32]

Q. WeiJ. M. Bioucas-DiasN. Dobigeon and J. Y. Tourneret, Hyperspectral and multispectral image fusion based on a sparse representation, IEEE Transactions on Geoscience and Remote Sensing, 53 (2015), 3658-3668.  doi: 10.1109/TGRS.2014.2381272.  Google Scholar

[33]

Q. WeiN. Dobigeon and J. Y. Tourneret, Fast fusion of multi-band images based on solving a Sylvester equation, IEEE Transactions on Image Processing, 24 (2015), 4109-4121.  doi: 10.1109/TIP.2015.2458572.  Google Scholar

[34]

W. WanJ. Liu and H. Huang, Local block operators and TV regularization based image inpainting, Inverse Problems and Imaging, 12 (2018), 1389-1410.  doi: 10.3934/ipi.2018058.  Google Scholar

[35]

Q. Xie, Q. Zhao, D. Meng, Z. Xu, S. Gu, W. Zuo and L. Zhang, Multispectral images denoising by intrinsic tensor sparsity regularization, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016). doi: 10.1109/CVPR.2016.187.  Google Scholar

[36]

Q. XieQ. ZhaoD. Meng and Z. Xu, Kronecker-basis-representation based tensor sparsity and its applications to tensor recovery, IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (2018), 1888-1902.  doi: 10.1109/TPAMI.2017.2734888.  Google Scholar

[37]

N. YokoyaT. Yairi and A. Iwasaki, Coupled nonnegative matrix factorization unmixing for hyperspectral and multispectral data fusion, IEEE Transactions on Geoscience and Remote Sensing, 50 (2012), 528-537.  doi: 10.1109/TGRS.2011.2161320.  Google Scholar

[38]

F. YasumaT. MitsunagaD. Iso and S. K. Nayar, Generalized assorted pixel camera: postcapture control of resolution, dynamic range, and spectrum, IEEE Transactions on Image Processing, 19 (2010), 2241-2253.  doi: 10.1109/TIP.2010.2046811.  Google Scholar

[39]

L. ZhangW. WeiC. BaiY. Gao and Y. Zhang, Exploiting clustering manifold structure for hyperspectral imagery super-resolution, IEEE Transactions on Image Processing, 27 (2018), 5969-5982.  doi: 10.1109/TIP.2018.2862629.  Google Scholar

[40]

Z. ZhangE. PasolliM. M. Crawford and J. C. Tilton, An active learning framework for hyperspectral image classification using hierarchical segmentation, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 9 (2016), 640-654.  doi: 10.1109/JSTARS.2015.2493887.  Google Scholar

[41]

H. ZhangJ. LiY. Huang and L. Zhang, A nonlocal weighted joint sparse representation classification method for hyperspectral imagery, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7 (2014), 2056-2065.   Google Scholar

[42]

H. ZhangH. ZhaiL. Zhang and P. Li, Spectral-spatial sparse subspace clustering for hyperspectral remote sensing images, IEEE Transactions on Geoscience and Remote Sensing, 54 (2016), 3672-3684.  doi: 10.1109/TGRS.2016.2524557.  Google Scholar

show all references

References:
[1]

N. Akhtar, F. Shafait and A. Mian, Bayesian sparse representation for hyperspectral image super resolution, IEEE Computer Vision and Pattern Recognition (CVPR), (2015), 3631-3640. doi: 10.1109/CVPR.2015.7298986.  Google Scholar

[2]

J. M. Bioucas-DiasA. PlazaG. Camps-VallsP. ScheundersN. Nasrabadi and J. Chanussot, Hyperspectral remote sensing data analysis and future challenges, IEEE Geoscience and Remote Sensing Magazine, 1 (2013), 6-36.  doi: 10.1109/MGRS.2013.2244672.  Google Scholar

[3]

J. M. Bioucas-Dias and A. Plaza, Hyperspectral unmixing: Geometrical, statistical, and sparse regression-based approaches, Image and Signal Processing for Remote Sensing XVI, (2010), 354-379. Google Scholar

[4]

Y. Chang, L. Yan, H. Fang, S. Zhong and Z. Zhang, Weighted Low-Rank Tensor Recovery for Hyperspectral Image Restoration, ARXIV, 2017. Google Scholar

[5]

C. F. Caiafa and A. Cichocki, Computing sparse representations of multidimensional signals using kronecker bases, Neural Computation, 25 (2013), 186-220.  doi: 10.1162/NECO_a_00385.  Google Scholar

[6]

W. DongF. FuG. ShiX. CaoJ. WuG. Li and X. Li, Hyperspectral image super-resolution via non-negative structured sparse representation, IEEE Transactions on Image Processing, 25 (2016), 2337-2352.  doi: 10.1109/TIP.2016.2542360.  Google Scholar

[7]

R. Dian, L. Fang and S. Li, Hyperspectral image super-resolution via non-local sparse tensor factorization, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017). doi: 10.1109/CVPR.2017.411.  Google Scholar

[8]

F. Dell''AcquaP. GambaA. FerrariJ. A. PalmasonJ. A. Benediktsson and K. Arnason, Exploiting spectral and spatial information in hyperspectral urban data with high resolution, IEEE Geoscience and Remote Sensing Letters, 1 (2004), 322-326.   Google Scholar

[9]

H. FanY. ChenY. GuoH. Zhang and G. Kuang, Hyperspectral image restoration using low-rank tensor recovery, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 10 (2017), 4589-4604.  doi: 10.1109/JSTARS.2017.2714338.  Google Scholar

[10]

A. F. H. Goetz, Three decades of hyperspectral remote sensing of the earth: A personal view, Remote Sensing of Environment, 113 (2009), S5-S16. doi: 10.1016/j.rse.2007.12.014.  Google Scholar

[11]

C. Jia and Y. Fu, Low-rank tensor subspace learning for RGB-D action recognition, IEEE Transactions on Image Processing, 25 (2016), 4641-4652.  doi: 10.1109/TIP.2016.2589320.  Google Scholar

[12]

C. JiaM. Shao and Y. Fu, Sparse canonical temporal alignment with deep tensor decomposition for action recognition, IEEE Transactions on Image Processing, 26 (2017), 738-750.  doi: 10.1109/TIP.2016.2621664.  Google Scholar

[13]

R. Kawakami, J. Wright, Y. W. Tai and Y. Matsushita, High-resolution hyperspectral imaging via matrix factorization, Computer Vision and Pattern Recognition (CVPR), (2011), 2329-2336. doi: 10.1109/CVPR.2011.5995457.  Google Scholar

[14]

C. I. KanatsoulisX. FuN. D. Sidiropoulos and W. K. Ma, Hyperspectral super-resolution: A coupled tensor factorization approach, IEEE Transactions on Signal Processing, 66 (2018), 6503-6517.  doi: 10.1109/TSP.2018.2876362.  Google Scholar

[15]

T. G. Kolda and B. W. Bader, Tensor decompositions and applications, Siam Review, 51 (2009), 455-500.  doi: 10.1137/07070111X.  Google Scholar

[16]

W. LiG. WuF. Zhang and Q. Du, Hyperspectral image classification using deep pixel-pair features, IEEE Transactions on Geoscience and Remote Sensing, 55 (2016), 844-853.   Google Scholar

[17]

X. LiuW. XiaB. Wang and L. Zhang, An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data, IEEE Transactions on Geoscience and Remote Sensing, 49 (2011), 757-772.  doi: 10.1109/TGRS.2010.2068053.  Google Scholar

[18]

S. LiR. DianL. Fang and J. M. Bioucas-Dias, Fusing hyperspectral and multispectral images via coupled sparse tensor factorization, IEEE Transactions on Image Processing, 27 (2018), 4118-4130.  doi: 10.1109/TIP.2018.2836307.  Google Scholar

[19]

M. J. Montag and H. Stephani, Hyperspectral unmixing from incomplete and noisy data, Journal of Imaging, 2 (2016), p7. doi: 10.3390/jimaging2010007.  Google Scholar

[20]

J. MaH. ZhouJ. ZhaoY. CaoJ. Jiang and J. Tian, Robust feature matching for remote sensing image registration via locally linear transforming, IEEE Transactions on Geoscience and Remote Sensing, 53 (2015), 6469-6481.  doi: 10.1109/TGRS.2015.2441954.  Google Scholar

[21]

H. V. Nguyen, A. Banerjee and R. Chellappa, Tracking via object reflectance using a hyperspectral video camera, IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Workshops, (2010). doi: 10.1109/CVPRW.2010.5543780.  Google Scholar

[22]

Y. Peng, D. Meng, Z. Xu, C. Cao, Y. Yang and B. Zhang, Decomposable nonlocal tensor dictionary learning for multispectral image denoising, IEEE Conference on Computer Vision and Pattern Recognition, (2014). doi: 10.1109/CVPR.2014.377.  Google Scholar

[23]

Y. QianF. XiongS. ZengJ. Zhou and Y. Y. Tang, Matrix-vector nonnegative tensor factorization for blind unmixing of hyperspectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 55 (2017), 1776-1792.   Google Scholar

[24]

M. SimoesJ. M. Bioucas-DiasL. B. Almeida and J. Chanussot, A convex formulation for hyperspectral image superresolution via subspace-based regularization, IEEE Transactions on Geoscience and Remote Sensing, 53 (2014), 3373-3388.  doi: 10.1109/TGRS.2014.2375320.  Google Scholar

[25]

S. SoltaniM. E. Kilmer and P. C. Hansen, A tensor-based dictionary learning approach to tomographic image reconstruction, BIT Numerical Mathematics, 56 (2016), 1425-1454.  doi: 10.1007/s10543-016-0607-z.  Google Scholar

[26]

Y. TarabalkaJ. Chanussot and J. A. Benediktsson, Segmentation and classification of hyperspectral images using minimum spanning forest grown from automatically selected markers, IEEE Transactions on Systems, Man, and Cybernetics, 40 (2010), 1267-1279.  doi: 10.1109/TSMCB.2009.2037132.  Google Scholar

[27]

X. C. Tai and C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, International Conference on Scale Space and Variational Methods in Computer Vision, (2009), 502-513. Google Scholar

[28]

M. UzairA. Mahmood and A. Mian, Hyperspectral face recognition using 3D-DCT and partial least squares, BMVC, 10 (2013), 1-57.  doi: 10.5244/C.27.57.  Google Scholar

[29]

M. UzairA. Mahmood and A. Mian, Hyperspectral face recognition with spatiospectral information fusion and PLS regression, IEEE Transactions on Image Processing, 24 (2015), 1127-1137.  doi: 10.1109/TIP.2015.2393057.  Google Scholar

[30]

G. VaneR. O. GreenT. G. ChrienH. T. EnmarkE. G. Hansen and W. M. Porter, The airborne visible/infrared imaging spectrometer (AVIRIS), Remote Sensing of Environment, 44 (1993), 127-143.  doi: 10.1016/0034-4257(93)90012-M.  Google Scholar

[31]

E. Wycoff, T. H. Chan, K. Jia, W. K. Ma and Y. Ma, A non-negative sparse promoting algorithm for high resolution hyperspectral imaging, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (2013), 1409-1413. doi: 10.1109/ICASSP.2013.6637883.  Google Scholar

[32]

Q. WeiJ. M. Bioucas-DiasN. Dobigeon and J. Y. Tourneret, Hyperspectral and multispectral image fusion based on a sparse representation, IEEE Transactions on Geoscience and Remote Sensing, 53 (2015), 3658-3668.  doi: 10.1109/TGRS.2014.2381272.  Google Scholar

[33]

Q. WeiN. Dobigeon and J. Y. Tourneret, Fast fusion of multi-band images based on solving a Sylvester equation, IEEE Transactions on Image Processing, 24 (2015), 4109-4121.  doi: 10.1109/TIP.2015.2458572.  Google Scholar

[34]

W. WanJ. Liu and H. Huang, Local block operators and TV regularization based image inpainting, Inverse Problems and Imaging, 12 (2018), 1389-1410.  doi: 10.3934/ipi.2018058.  Google Scholar

[35]

Q. Xie, Q. Zhao, D. Meng, Z. Xu, S. Gu, W. Zuo and L. Zhang, Multispectral images denoising by intrinsic tensor sparsity regularization, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016). doi: 10.1109/CVPR.2016.187.  Google Scholar

[36]

Q. XieQ. ZhaoD. Meng and Z. Xu, Kronecker-basis-representation based tensor sparsity and its applications to tensor recovery, IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (2018), 1888-1902.  doi: 10.1109/TPAMI.2017.2734888.  Google Scholar

[37]

N. YokoyaT. Yairi and A. Iwasaki, Coupled nonnegative matrix factorization unmixing for hyperspectral and multispectral data fusion, IEEE Transactions on Geoscience and Remote Sensing, 50 (2012), 528-537.  doi: 10.1109/TGRS.2011.2161320.  Google Scholar

[38]

F. YasumaT. MitsunagaD. Iso and S. K. Nayar, Generalized assorted pixel camera: postcapture control of resolution, dynamic range, and spectrum, IEEE Transactions on Image Processing, 19 (2010), 2241-2253.  doi: 10.1109/TIP.2010.2046811.  Google Scholar

[39]

L. ZhangW. WeiC. BaiY. Gao and Y. Zhang, Exploiting clustering manifold structure for hyperspectral imagery super-resolution, IEEE Transactions on Image Processing, 27 (2018), 5969-5982.  doi: 10.1109/TIP.2018.2862629.  Google Scholar

[40]

Z. ZhangE. PasolliM. M. Crawford and J. C. Tilton, An active learning framework for hyperspectral image classification using hierarchical segmentation, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 9 (2016), 640-654.  doi: 10.1109/JSTARS.2015.2493887.  Google Scholar

[41]

H. ZhangJ. LiY. Huang and L. Zhang, A nonlocal weighted joint sparse representation classification method for hyperspectral imagery, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7 (2014), 2056-2065.   Google Scholar

[42]

H. ZhangH. ZhaiL. Zhang and P. Li, Spectral-spatial sparse subspace clustering for hyperspectral remote sensing images, IEEE Transactions on Geoscience and Remote Sensing, 54 (2016), 3672-3684.  doi: 10.1109/TGRS.2016.2524557.  Google Scholar

Figure 1.  Illustration of the hyperspectral image super-resolution task
Figure 2.  The SAMs of all competing methods on CAVE dataset with uniform blur
Figure 3.  The reconstructed images and the corresponding error images of fake and real peppers at the $ 8^{th} $ band and flowers at the $ 14^{th} $ band with Gaussian blur and scaling factor 8
Figure 4.  The reconstructed images and the corresponding error images of the Indian Pines image at the $ 60^{th} $ and $ 130^{th} $ bands with uniform blur and scaling factor 8
Figure 5.  The functional energy curve for the proposed algorithm
Figure 6.  The reconstructed images and the corresponding error images of the Pavia image at the $ 45^{th} $ and $ 75^{th} $ bands with uniform blur and scaling factor 8
Table 1.  Comparison on the average values of each of the five quantitative measures on 32 scenes from CAVE dataset with scaling factor 8
Methods PSNR SSIM RMSE SAM ERGAS
Uniform blur
CNMF[37] 43.052 0.985 2.299 5.934 1.224
Hysure[24] 41.461 0.975 2.702 10.737 1.497
STEREO[14] 39.680 0.946 3.611 12.212 1.898
Proposed 45.332 0.987 1.822 4.969 0.984
Gaussian blur
CNMF[37] 42.258 0.981 2.511 6.578 1.329
Hysure[24] 41.961 0.977 2.541 10.310 1.425
STEREO[14] 39.542 0.945 3.658 12.251 1.923
Proposed 45.206 0.987 1.847 4.983 0.995
Methods PSNR SSIM RMSE SAM ERGAS
Uniform blur
CNMF[37] 43.052 0.985 2.299 5.934 1.224
Hysure[24] 41.461 0.975 2.702 10.737 1.497
STEREO[14] 39.680 0.946 3.611 12.212 1.898
Proposed 45.332 0.987 1.822 4.969 0.984
Gaussian blur
CNMF[37] 42.258 0.981 2.511 6.578 1.329
Hysure[24] 41.961 0.977 2.541 10.310 1.425
STEREO[14] 39.542 0.945 3.658 12.251 1.923
Proposed 45.206 0.987 1.847 4.983 0.995
Table 2.  The performance comparison of the methods on the Indian Pines image with scaling factor 8
Methods PSNR SSIM RMSE SAM ERGAS
Uniform blur
CNMF[37] 42.866 0.978 2.557 2.394 9.406
Hysure[24] 45.232 0.984 1.891 1.701 9.389
STEREO[14] 48.212 0.985 1.267 1.225 9.405
Proposed 51.441 0.993 0.928 0.888 9.368
Gaussian blur
CNMF[37] 42.740 0.977 2.599 2.430 9.409
Hysure[24] 45.927 0.986 1.703 1.547 9.384
STEREO[14] 47.050 0.981 1.510 1.413 9.438
Proposed 51.326 0.993 0.950 0.904 9.369
Methods PSNR SSIM RMSE SAM ERGAS
Uniform blur
CNMF[37] 42.866 0.978 2.557 2.394 9.406
Hysure[24] 45.232 0.984 1.891 1.701 9.389
STEREO[14] 48.212 0.985 1.267 1.225 9.405
Proposed 51.441 0.993 0.928 0.888 9.368
Gaussian blur
CNMF[37] 42.740 0.977 2.599 2.430 9.409
Hysure[24] 45.927 0.986 1.703 1.547 9.384
STEREO[14] 47.050 0.981 1.510 1.413 9.438
Proposed 51.326 0.993 0.950 0.904 9.369
Table 3.  The performance comparison of noisy cases on the Pavia image with uniform blur and scaling factor 8
Methods PSNR SSIM RMSE SAM ERGAS
SNRh=35dB, SNRm=40dB
CNMF[37] 37.958 0.982 3.335 2.790 0.958
Hysure[24] 42.573 0.987 2.278 2.420 0.584
STEREO[14] 37.307 0.951 3.715 4.022 1.039
Proposed 43.731 0.989 1.848 1.944 0.497
SNRh=30dB, SNRm=35dB
CNMF[37] 37.694 0.979 3.439 2.885 0.979
Hysure[24] 41.541 0.982 2.338 2.553 0.644
STEREO[14] 35.584 0.932 4.401 4.829 1.252
Proposed 42.097 0.981 2.158 2.349 0.604
Methods PSNR SSIM RMSE SAM ERGAS
SNRh=35dB, SNRm=40dB
CNMF[37] 37.958 0.982 3.335 2.790 0.958
Hysure[24] 42.573 0.987 2.278 2.420 0.584
STEREO[14] 37.307 0.951 3.715 4.022 1.039
Proposed 43.731 0.989 1.848 1.944 0.497
SNRh=30dB, SNRm=35dB
CNMF[37] 37.694 0.979 3.439 2.885 0.979
Hysure[24] 41.541 0.982 2.338 2.553 0.644
STEREO[14] 35.584 0.932 4.401 4.829 1.252
Proposed 42.097 0.981 2.158 2.349 0.604
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