Spatial-Spectral Adaptive Fidelity and Noise Prior Reduction Guided Hyperspectral Image Denoising

Xuelin Xie; Xiliang Lu; Zhengshan Wang; Yang Zhang; Long Chen

cs.CVApr 14, 2026

Spatial-Spectral Adaptive Fidelity and Noise Prior Reduction Guided Hyperspectral Image Denoising

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

Abstract

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
$\mathbf{Y}/\mathcal{Y}\hskip 16.00008pt$	Noisy HSI matrix/tensor.
$\mathbf{X}/\mathcal{X}$	Restored HSI matrix/tensor.
$\mathbf{N}/\mathcal{N}$	Noise matrix/tensor.
$\mathbf{S}/\mathcal{S}$	Sparse noise matrix/tensor.
$\mathbf{D}/\mathcal{D}$	Deadline or stripe noise/tensor.
$\mathbf{W}/\mathcal{W}$	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 $\ell_{1}$ -norm Prior	✗	✓	✓	✗	✓	✗	✓	✓	✓	✓	✓
Structured $\ell_{2,1}$ -norm Prior	✗	✗	✗	✗	✗	✓	✗	✗	✗	✗	✓
TV Regularization	✓	✓	✗	✗	✓	✗	✓	✓	✓	✓	✓
RCTV Regularization	✗	✗	✗	✗	✗	✗	✗	✓	✗	✗	✓

Table 2: Comparison of Methodological Properties.

Figure 3: Explanation of the adaptive pixel-wise weighting strategy.

Panel of Figure 4 — 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 $(200\times 200\times 31)$	Case 1 G:0.1+S:0.15	PSNR $\uparrow$	12.1544	24.6370	31.1530	31.2021	28.9673	31.0676	30.1415	28.2611	21.0550	31.8896
		SSIM $\uparrow$	0.1125	0.7956	0.8271	0.9139	0.9011	0.9194	0.8493	0.8339	0.3994	0.9195
		SAM $\downarrow$	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 $\uparrow$	17.2448	25.0311	26.0098	26.3044	24.4271	26.5381	25.7595	24.0865	22.8881	25.0156
		SSIM $\uparrow$	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.

Panel of Figure 7 — Figure 7: Sensitivity analysis of FRHD model parameter $r$ under different noise conditions for three datasets.

Panel of Figure 8 — Figure 8: Sensitivity analysis of FRHD model parameter $\tau$ under different noise conditions for three datasets.

Panel of Figure 9 — Figure 9: Sensitivity of FRHD model parameters $\beta$ and $\gamma$ 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
Cases	$r$	$\tau$	$[\beta,\gamma]$	$r$	$\tau$	$[\beta,\gamma]$	$r$	$\tau$	$[\beta,\gamma]$
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 $\Uparrow$	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 $\Uparrow$	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.

Figure 10: Gradient Experiment (Gradually Intensifying Salt-and-Pepper Noise).

Figure 11: Gradient Experiment (5% Salt-and-Pepper + 5% Stripes + Gradually Intensifying Gaussian Noise).

Cases	Noisy				HLRTF [ 48 ]				Flex-DLD [ 10 ]				FRHD
Cases	PSNR	SSIM	SAM	Time	PSNR	SSIM	SAM	Time	PSNR	SSIM	SAM	Time	PSNR	SSIM	SAM	Time
Case 1	12.36	0.1543	0.7534	0.00	31.43	0.9316	0.0803	17.98	31.14	0.9158	0.0811	89.62	35.22	0.9522	0.0652	5.73
Case 2	17.14	0.2912	0.6340	0.00	32.19	0.9319	0.0778	17.09	27.11	0.8513	0.1247	89.57	29.26	0.9114	0.0959	9.73
Case 3	11.55	0.1106	0.8674	0.00	27.90	0.8266	0.1356	15.79	26.42	0.8224	0.1296	89.49	29.00	0.8749	0.1168	7.59
Case 4	11.42	0.1027	0.8934	0.00	27.85	0.8501	0.1167	16.38	25.05	0.7961	0.1534	89.33	27.07	0.8650	0.1197	7.60
Case 5	11.61	0.1095	0.8714	0.00	29.14	0.8956	0.0995	17.34	25.79	0.8122	0.1446	91.01	27.87	0.8704	0.1188	7.53

Table 6: Comparison results on WDC dataset. Best and second-best results are highlighted in bold and underline , respectively.

Panel of Figure 12 — Figure 12: Iteration results of FRHD method on different simulated datasets. (a) CAVE dataset; (b) PaC dataset; (c) WDC dataset.

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Deep Image Prior Image Denoising Self-Supervised Image Denoising

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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

\ell_1

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.

Abstract

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