A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising
Abstract
:1. Introduction
- By treating an HSI as a 3D cube, 3D anisotropic total variation (3DATV) is adopted to exploit the spatial smoothness and spectral consistency simultaneously along with the low-rank regularization.
- The TV denoising process is updated iteratively in a spatial-spectral manner in the alternating direction method of multipliers (ADMM) algorithm instead of in a band-by-band manner, and it can be effectively solved by an n-D fast Fourier transform (nFFT).
- When low-rank regularization fails to remove the structured sparse noise, i.e., structured stripes or dead lines, 3DATV could effectively get rid of them by simultaneously exploring the spatial and spectral consistency while LRTV even makes this case in a dilemma since the band-by-band TV preserves the stripes or deadlines along one of the directions.
2. Basic Formulation
2.1. Observation Model
2.2. Restoration Model
2.3. Prior Regularizations
2.3.1. Low Rank Regularization
- Due to the independent distribution of Gaussian noise in each pixel, Equation (3) can not completely remove the heavy Gaussian noise.
- Equation (3) can not remove the structured sparse noise, i.e., stripes or dead lines locate at the same place in each band because the low rank method will treat them as one of the low rank components.
2.3.2. Total Variation Regularization
3. 3D Anisotropic TV Regularized Low-Rank Model for HSI Restoration
3.1. 3D Anisotropic Total Variation Regularization
3.2. Proposed 3DATVLR Model
3.3. Optimization Algorithm
Algorithm 1 Extended ADMM for the 3DATVLR method. |
|
3.4. Parameters Determination
4. Experimental Results and Discussion
4.1. Comparison Methods and Assessment Metrics
4.2. Experiments on Simulated Datasets
4.2.1. Datasets and Experimental Settings
- (1)
- Case 1: Zero-mean Gaussian noise with the same variance of 0.01 was added to each band.
- (2)
- Case 2: Zero-mean Gaussian noise with the same variance of 0.01, as well as the impulse noise with the same density of 15%, was added to each band.
- (3)
- Case 3: In this case, the Gaussian noise and impulse noise were added just like that in Case 2. In addition, the deadlines were added from band 111 to band 150 with the number of deadlines being randomly selected from 3 to 10, and the width of each deadline was randomly generated from 1 to 3.
- (4)
- Case 4: In this case, the noise intensity was different for each band. First, zero-mean Gaussian noise with different variances varying from 0 to 0.02 was added to each band randomly. Second, impulse noise with a density percentage varying from 0 to 20% was randomly added to each band. Finally, dead lines were simulated the same as that in Case 3.
- (5)
- Case 5: In this case, the Gaussian noise, impulse noise and dead lines are simulated the same as that in Case 4. In addition, some periodical stripes are added from band 146 to 165; the number of stripes in each band is 30.
- (6)
- Case 6: In this case, the Gaussian noise, impulse noise and stripes are simulated the same as that in Case 5. However, the dead lines are simulated to be located in the same place as the 40 bands randomly selected from all of the bands; the number of dead lines in each band is 15. This case is to simulate the structured sparse noise for the most severe noise situation.
4.2.2. Visual Performance Evaluation
4.2.3. Quantitative Performance Evaluation
4.2.4. Parameters’ Sensitive Analysis
4.3. Experiments on a Real Dataset
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Noise | BM4D | PCABM4D | PARAFAC | 3DTV | TDL | LRMR | LRTV | 3DATVLR |
---|---|---|---|---|---|---|---|---|
Case 1 | - | - | rank(L) = 5 | |||||
card(s) = 0.0 | ||||||||
Case 2 | - | - | rank(L) = 5 | |||||
card(s) = 0.04 | ||||||||
Case 3 | - | - | rank(L) = 5 | |||||
card(s) = 0.07 | ||||||||
Case 4 | - | - | rank(L) = 5 | |||||
card(s) = 0.07 | ||||||||
Case 5 | - | - | rank(L) = 5 | |||||
card(s) = 0.06 | ||||||||
Case 6 | - | - | rank(L) = 5 | |||||
card(s) = 0.05 | ||||||||
Noise | Metrics | Noisy | BM4D | PCABM4D | PARAFAC | 3DTV | TDL | LRMR | LRTV | 3DATVLR |
---|---|---|---|---|---|---|---|---|---|---|
Case 1 | MPSNR (dB) | 20.12 | 37.91 | 41.22 | 31.92 | 33.32 | 37.24 | 37.91 | 38.24 | 40.32 |
MSSIM | 0.3710 | 0.9695 | 0.9876 | 0.8946 | 0.9395 | 0.9758 | 0.9695 | 0.9884 | 0.9909 | |
MFSIM | 0.4724 | 0.9617 | 0.9860 | 0.8655 | 0.9344 | 0.9635 | 0.9617 | 0.9863 | 0.9885 | |
ERGAS | 230.15 | 30.72 | 21.00 | 61.97 | 69.23 | 33.17 | 30.72 | 29.93 | 23.91 | |
MSA | 0.1949 | 0.0234 | 0.0158 | 0.0391 | 0.0497 | 0.0201 | 0.0234 | 0.0174 | 0.0161 | |
Case 2 | MPSNR (dB) | 12.78 | 28.50 | 28.36 | 25.70 | 32.14 | 26.88 | 35.12 | 38.13 | 39.24 |
MSSIM | 0.1682 | 0.8534 | 0.9287 | 0.6819 | 0.9183 | 0.9030 | 0.9168 | 0.9844 | 0.9894 | |
MFSIM | 0.3397 | 0.8535 | 0.9372 | 0.7047 | 0.9140 | 0.8876 | 0.9156 | 0.9774 | 0.9868 | |
ERGAS | 538.15 | 91.90 | 93.51 | 125.09 | 78.58 | 110.59 | 42.00 | 30.57 | 26.79 | |
MSA | 0.4268 | 0.0673 | 0.0682 | 0.0937 | 0.0568 | 0.0805 | 0.0282 | 0.0198 | 0.0179 | |
Case 3 | MPSNR (dB) | 12.63 | 26.93 | 26.83 | 24.48 | 32.03 | 26.18 | 34.62 | 37.30 | 38.50 |
MSSIM | 0.1656 | 0.8100 | 0.8437 | 0.6698 | 0.9259 | 0.8390 | 0.9112 | 0.9781 | 0.9892 | |
MFSIM | 0.3372 | 0.8269 | 0.8653 | 0.7015 | 0.9236 | 0.8483 | 0.9099 | 0.9744 | 0.9866 | |
ERGAS | 547.23 | 128.70 | 116.59 | 161.51 | 80.27 | 122.68 | 44.59 | 54.83 | 29.29 | |
MSA | 0.4364 | 0.0997 | 0.0884 | 0.1289 | 0.0574 | 0.0893 | 0.0318 | 0.0430 | 0.0197 | |
Case 4 | MPSNR (dB) | 14.26 | 27.62 | 27.27 | 25.62 | 33.16 | 24.46 | 34.06 | 36.09 | 39.02 |
MSSIM | 0.2236 | 0.7976 | 0.8169 | 0.7171 | 0.9373 | 0.6328 | 0.9249 | 0.9724 | 0.9924 | |
MFSIM | 0.3920 | 0.8207 | 0.8253 | 0.7304 | 0.9354 | 0.6870 | 0.9211 | 0.9737 | 0.9915 | |
ERGAS | 486.26 | 174.99 | 154.37 | 189.63 | 72.96 | 189.56 | 67.05 | 74.54 | 29.46 | |
MSA | 0.3969 | 0.1422 | 0.1237 | 0.1597 | 0.0515 | 0.1518 | 0.0478 | 0.0578 | 0.0202 | |
Case 5 | MPSNR (dB) | 13.94 | 26.92 | 26.86 | 24.87 | 33.19 | 25.24 | 34.76 | 36.40 | 39.19 |
MSSIM | 0.2123 | 0.7635 | 0.7946 | 0.6801 | 0.9339 | 0.6845 | 0.9323 | 0.9829 | 0.9921 | |
MFSIM | 0.3802 | 0.8007 | 0.8098 | 0.7113 | 0.9334 | 0.7392 | 0.9285 | 0.9843 | 0.9911 | |
ERGAS | 493.39 | 172.68 | 146.17 | 189.80 | 71.39 | 169.86 | 54.56 | 55.00 | 28.21 | |
MSA | 0.4028 | 0.1410 | 0.1160 | 0.1594 | 0.0509 | 0.1316 | 0.0392 | 0.0398 | 0.0192 | |
Case 6 | MPSNR (dB) | 14.28 | 26.78 | 27.59 | 25.14 | 33.32 | 25.18 | 32.10 | 33.86 | 36.73 |
MSSIM | 0.2197 | 0.7328 | 0.8338 | 0.6559 | 0.9333 | 0.6592 | 0.8526 | 0.8999 | 0.9817 | |
MFSIM | 0.3912 | 0.7908 | 0.8793 | 0.7109 | 0.9327 | 0.7320 | 0.8902 | 0.9427 | 0.9841 | |
ERGAS | 481.82 | 161.46 | 169.65 | 191.34 | 72.67 | 189.90 | 154.02 | 156.26 | 53.69 | |
MSA | 0.3903 | 0.1069 | 0.0988 | 0.1281 | 0.0511 | 0.1245 | 0.0682 | 0.0751 | 0.0370 | |
runtime (s) | - | 194.1 | 195.0 | 353.0 | 76.0 | 11.3 | 28.0 | 79.7 | 40.8 |
Methods | Original | 3DTV | LRMR | LRTV | 3DATVLR |
---|---|---|---|---|---|
aQ | 60.78 | 61.44 | 62.38 | 62.84 | 65.13 |
Times (s) | - | 3590 | 2811 | 549 | 648 |
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Sun, L.; Zhan, T.; Wu, Z.; Jeon, B. A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising. ISPRS Int. J. Geo-Inf. 2018, 7, 412. https://doi.org/10.3390/ijgi7100412
Sun L, Zhan T, Wu Z, Jeon B. A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising. ISPRS International Journal of Geo-Information. 2018; 7(10):412. https://doi.org/10.3390/ijgi7100412
Chicago/Turabian StyleSun, Le, Tianming Zhan, Zebin Wu, and Byeungwoo Jeon. 2018. "A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising" ISPRS International Journal of Geo-Information 7, no. 10: 412. https://doi.org/10.3390/ijgi7100412