Hyperspectral Image Restoration Using Low-Rank Representation on Spectral Difference Image

This letter presents a novel mixed noise (i.e., Gaussian, impulse, stripe noises, or dead lines) reduction method for hyperspectral image (HSI) by utilizing low-rank representation (LRR) on spectral difference image. The proposed method is based on the assumption that all spectra in the spectral difference space of HSI lie in the same low-rank subspace. The LRR on the spectral difference space was exploited by nuclear norm of difference image along the spectral dimension. It showed great potential in removing structured sparse noise (e.g., stripes or dead lines located at the same place of each band) and heavy Gaussian noise. To simultaneously solve the proposed model and reduce computational load, alternating direction method of multipliers was utilized to achieve robust reconstruction. The experimental results on both simulated and real HSI data sets validated that the proposed method outperformed many state-of-the-art methods in terms of quantitative assessment and visual quality.

[1]  Jocelyn Chanussot,et al.  Hyperspectral Super-Resolution of Locally Low Rank Images From Complementary Multisource Data , 2014, IEEE Transactions on Image Processing.

[2]  Yulong Wang,et al.  Graph-Regularized Low-Rank Representation for Destriping of Hyperspectral Images , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[3]  Yang Xu,et al.  Spectral-Spatial Classification of Hyperspectral Image Based on Low-Rank Decomposition , 2015, IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens..

[4]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[5]  Jing-Hao Xue,et al.  Spectral Nonlocal Restoration of Hyperspectral Images With Low-Rank Property , 2015, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[6]  Karen O. Egiazarian,et al.  Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction , 2013, IEEE Transactions on Image Processing.

[7]  Liangpei Zhang,et al.  Hyperspectral Image Denoising via Noise-Adjusted Iterative Low-Rank Matrix Approximation , 2015, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[8]  Dacheng Tao,et al.  GoDec: Randomized Lowrank & Sparse Matrix Decomposition in Noisy Case , 2011, ICML.

[9]  Yuhui Zheng,et al.  Hyperspectral restoration employing low rank and 3D total variation regularization , 2016, 2016 International Conference on Progress in Informatics and Computing (PIC).

[10]  C. Grimes,et al.  GULF OF MEXICO , 1997 .

[11]  Liangpei Zhang,et al.  Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Jing-Hao Xue,et al.  Denoising of Hyperspectral Images Using Group Low-Rank Representation , 2016, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[13]  Jonathan Eckstein,et al.  Understanding the Convergence of the Alternating Direction Method of Multipliers: Theoretical and Computational Perspectives , 2015 .

[14]  Liangpei Zhang,et al.  Hyperspectral Image Restoration Using Low-Rank Matrix Recovery , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[15]  Paris V. Giampouras,et al.  Simultaneously Sparse and Low-Rank Abundance Matrix Estimation for Hyperspectral Image Unmixing , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[16]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.