Authors: Xuelin Xie, Xiliang Lu, Zhengshan Wang, Yang Zhang, Long Chen
Organizations: School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China · Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, 999078, Macau, China · Hubei Center for Applied Mathematics, Wuhan University, Wuhan, 430072, China · Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China
The core challenge of hyperspectral image denoising is striking the right balance between data fidelity and noise prior modeling. Most existing methods place too much emphasis on the intrinsic priors of the image while overlooking diverse noise assumptions and the dynamic trade-off between fidelity and priors. To address these issues, we propose a denoising framework that integrates noise prior reduction and a spatial-spectral adaptive fidelity term. This framework considers comprehensive noise priors with fewer parameters and introduces an adaptive weight tensor to dynamically balance the fidelity and prior regularization terms. Within this framework, we further develop a fast and robust pixel-wise model combined with the representative coefficient total variation regularizer to accurately remove mixed noise in HSIs. The proposed method not only efficiently handles various types of noise but also accurately captures the spectral low-rank structure and local smoothness of HSIs. An efficient optimization algorithm based on the alternating direction method of multipliers is designed to ensure stable and fast convergence. Extensive experiments on simulated and real-world datasets demonstrate that the proposed model achieves superior denoising performance while maintaining competitive computational efficiency.
Figures & tables
Notation
Definition
Y/Y
Noisy HSI matrix/tensor.
X/X
Restored HSI matrix/tensor.
N/N
Noise matrix/tensor.
S/S
Sparse noise matrix/tensor.
D/D
Deadline or stripe noise/tensor.
W/W
Weight matrix/tensor.
Table 1: The main symbols and their definitions.
Figure 1: Description of the three different types of noise.
Property
SSAHTV [ 23 ]
LRTV [ 35 ]
FastHyDe [ 36 ]
NGmeet [ 9 ]
LSSTV [ 37 ]
WLRTR [ 28 ]
WNLRATV [ 31 ]
RCTV [ 30 ]
TPTV [ 32 ]
CTV-SPCP [ 33 ]
FRHD Ours
Spectral Low-Rank
✗
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Gauss Noise Prior
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Sparse ℓ1 -norm Prior
✗
✓
✓
✗
✓
✗
✓
✓
✓
✓
✓
Structured ℓ2,1 -norm Prior
✗
✗
✗
✗
✗
✓
✗
✗
✗
✗
✓
TV Regularization
✓
✓
✗
✗
✓
✗
✓
✓
✓
✓
✓
RCTV Regularization
✗
✗
✗
✗
✗
✗
✗
✓
✗
✗
✓
Table 2: Comparison of Methodological Properties.
Figure 3: Explanation of the adaptive pixel-wise weighting strategy.
Figure 4: Five different levels of mixed noise pollution on the CAVE datasets, the R, G, and B channels correspond to spectral bands 14, 23, and 16, respectively. (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4; (e) Case 5.
Figure 5: Denoising results of all competing methods on the simulated datasets under Case 5. The pseudo-color images are visualized using spectral bands 14/23/16 (CAVE), 6/20/50 (PaC), and 152/106/20 (WDC) for the R-G-B channels, respectively.
Datasets
Case
Indexes
Noisy
SDeCNN [ 12 ]
WNLRATV [ 31 ]
RCTV [ 30 ]
FastHyMix [ 21 ]
TPTV [ 32 ]
CTV-SPCP [ 33 ]
FBGND [ 46 ]
FallHyDe [ 47 ]
FRHD Ours
CAVE dataset (200×200×31)
Case 1 G:0.1+S:0.15
PSNR ↑
12.1544
24.6370
31.1530
31.2021
28.9673
31.0676
30.1415
28.2611
21.0550
31.8896
SSIM ↑
0.1125
0.7956
0.8271
0.9139
0.9011
0.9194
0.8493
0.8339
0.3994
0.9195
SAM ↓
0.8056
0.1967
0.1887
0.1381
0.1933
0.1910
0.1598
0.1949
0.3357
0.1202
Time
–
5.4347
69.3791
0.9321
0.2315
11.9730
6.4013
323.4148
0.0401
0.6290
Case 2 G:0.1+D:0.2
PSNR ↑
17.2448
25.0311
26.0098
26.3044
24.4271
26.5381
25.7595
24.0865
22.8881
25.0156
SSIM ↑
0.2087
0.8381
0.8125
0.8219
0.7570
0.8272
0.7835
0.6979
0.6454
0. 8277
Table 3: Comparison of Denoising Methods on Simulated datasets. Best and second-best results are highlighted in bold and underline , respectively.
Figure 6: Denoising results of all competing methods on the HYDICE Urban city dataset. The R-G-B channels of the color image are composed of spectral bands 2, 150, and 206, respectively.
Figure 7: Sensitivity analysis of FRHD model parameter r under different noise conditions for three datasets.
Figure 8: Sensitivity analysis of FRHD model parameter τ under different noise conditions for three datasets.
Figure 9: Sensitivity of FRHD model parameters β and γ to CAVE dataset under different noise conditions. (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4; (e) Case 5.
Cases
CAVE
PaC
WDC
r
τ
[β,γ]
r
τ
[β,γ]
r
τ
[β,γ]
Case 1
4
1
[1, 0]
3
0.5
[0.95, 0]
5
0.47
[1.05, 0]
Case 2
4
3
[2.1, 1]
3
0.001
[1.3, 0.7]
4
0.001
[1.3, 0.7]
Cases 3-5
3
2.5
[1.5, 2.5]
3
1
[1.5, 2.5]
3
0.1
[1.5, 2.5]
Table 4: Parameter settings for CAVE, PaC, and WDC datasets across different cases.
Datasets
CAVE
PaC
WDC
Ablation Module
PSNR
SSIM
SAM
Time
PSNR
SSIM
SAM
Time
PSNR
SSIM
SAM
Time
Noisy
11.6046
0.0836
0.9221
–
11.7823
0.0724
0.9357
–
11.6066
0.1095
0.8714
–
RCTV
25.0842
0.7789
0.1997
0.9060
26.1311
0.7786
0.1555
5.7939
26.3929
0.8527
0.1286
7.3243
Baseline
23.9373
0.7696
0.1887
0.5655
25.6765
0.7779
0.1412
4.3299
25.7742
0.8246
0.1439
4.6729
Baseline+A ⇑
24.8229
0.8172
0.1681
0.7323
28.0799
0.8215
0.1110
4.9823
26.7997
0.8563
0.1159
6.4919
Baseline+A+B ⇑
25.7411
0.8242
0.1694
0.8567
29.1734
0.8275
0.1172
5.4872
27.8692
0.8704
0.1188
7.5402
Table 5: Denoising performance comparison of each module in the proposed FRHD against the Baseline model.
Deep image prior (DIP) is an unsupervised deep learning framework that has been successfully applied to a variety of inverse imaging problems. However, DIP-based methods are inherently prone to overfitting, which leads to performance degradation and necessitates early stopping. In this paper, we propose a method to mitigate overfitting in DIP-based hyperspectral image (HSI) denoising by jointly combining robust data fidelity and explicit sensitivity regularization. The proposed approach employs a Smooth ℓ1 data term together with a divergence-based regularization and input optimization during training. Experimental results on real HSIs corrupted by Gaussian, sparse, and stripe noise demonstrate that the proposed method effectively prevents overfitting and achieves superior denoising performance compared to state-of-the-art DIP-based HSI denoising methods.
Panagiotis Gkotsis, Athanasios A. Rontogiannis
Robotics Institute, Athena Research and Innovation Center, 151 25 Maroussi, Greece · School of Electrical and Computer Engineering, National Technical University of Athens, 157 80 Athens, Greece
Hyperspectral images (HSIs) are often degraded by mixed noise, including band-dependent Gaussian perturbations and structured artifacts such as stripes, dead-lines, and impulse noise. Most deep denoisers regress the clean image directly, entangling signal and structured noise. We instead model HSI denoising as \Y=\A\X+\Snoise+\Nnoise, where \A\X is a low-rank spectral-subspace (unmixing) reconstruction, \Snoise is structured sparse noise and \Nnoise is residual Gaussian noise. The resulting regularized optimization problem is unrolled into AXS-Net, a K-stage alternating proximal-point framework. Each stage combines an analytic spectral-basis gradient step, an SSX-Block proximal operator for abundance coefficients, and an SBlock proximal operator for the structured residual with column-consistent and sparse priors. This optimization correspondence exposes interpretable endmembers, abundance maps, and structured-noise estimates. Across ICVL, CAVE, and Harvard datasets and five noise configurations, the proposed AXS-Net achieves strong in-domain accuracy and competitive zero-shot transfer, with consistent gains across all five noise regimes on ICVL and Harvard. The recovered structured-noise closely follows the synthetic reference, and the recovered spectral basis is smooth and band-ordered rather than an arbitrary set of latent channels.
Hyperspectral image restoration faces several challenges, including limited training data, strong sensor specificity, and high spectral dimensionality. These limitations hinder the learning of robust hyperspectral priors, motivating the reuse of priors learned from large-scale RGB data. In this work, we propose a minimally trained, lightweight adapter that repurposes frozen pretrained RGB denoisers for hyperspectral restoration through a projection mapping. The method denoises low-dimensional spectral projections and reconstructs the hyperspectral cube through constrained linear aggregation, while preserving plug-and-play compatibility and the stability properties of the underlying RGB denoiser. Experiments on denoising, deblurring, and super-resolution across multiple datasets demonstrate consistent improvements over hyperspectral-specific baselines, showing the strong transferability of large-scale RGB priors.
Daniele Picone, Mohamad Jouni, Mauro Dalla-Mura
Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France