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Hybrid Noise Removal in Hyperspectral Imagery With a Spatial-Spectral Gradient Network

Qiang Zhang, Qiangqiang Yuan, Jie Li, Xinxin Liu, Huanfeng Shen, Liangpei Zhang

arXiv:1810.00495v3cs.CV

TL;DR

Hybrid noise in HSIs degrades data quality, interpretation accuracy, and subsequent applications. The paper proposes SSGN, which combines spatial-spectral gradient learning with fully cascaded multi-scale convolutional processing for mixed-noise removal. Across simulated and real experiments, SSGN outperforms other state-of-the-art denoising methods on evaluation indices, visual assessments, classification accuracy, and runtime.

  • Problem

    Hybrid HSI noise varies across spatial and spectral domains and can degrade interpretation and downstream applications, while existing methods may require manual tuning and leave residual noise or spectral distortion.

  • Method

    SSGN jointly uses spatial and adjacent spectral gradients with fully cascaded multi-scale convolutional blocks to remove mixed noise using one model across different HSIs or spectra.

  • Results

    SSGN outperforms other HSI denoising algorithms across most evaluation indices, visual assessments, classification accuracy, and time consumption under different mixed-noise scenarios.

  • Takeaways & Limitations

    SSGN provides a data-driven unified framework for efficiently handling multiple mixed-noise scenarios without manually adjusting presupposed parameters.

Abstract

from arXiv · show

The existence of hybrid noise in hyperspectral images (HSIs) severely degrades the data quality, reduces the interpretation accuracy of HSIs, and restricts the subsequent HSIs applications. In this paper, the spatial-spectral gradient network (SSGN) is presented for mixed noise removal in HSIs. The proposed method employs a spatial-spectral gradient learning strategy, in consideration of the unique spatial structure directionality of sparse noise and spectral differences with additional complementary information for better extracting intrinsic and deep features of HSIs. Based on a fully cascaded multi-scale convolutional network, SSGN can simultaneously deal with the different types of noise in different HSIs or spectra by the use of the same model. The simulated and real-data experiments undertaken in this study confirmed that the proposed SSGN performs better at mixed noise removal than the other state-of-the-art HSI denoising algorithms, in evaluation indices, visual assessments, and time consumption.

I. INTRODUCTION

HSIs are valuable for analysis but are degraded by diverse spatial-spectral noise, motivating a universal method for mixed-noise removal and band preservation. SSGN addresses this need by combining spatial-spectral gradient learning with a fully cascaded multi-scale convolutional network.

  • HSI noise from sensor instability and atmospheric interference can limit subsequent processing, making noise reduction important before interpretation and applications.
  • Existing methods require careful manual parameter adjustment for different HSI data and sensors, reducing convenience, universality, and efficiency.
  • Mixed noise varies across spatial and spectral domains, and existing algorithms may leave residual noise or cause spectral distortion.
  • The method is designed to handle Gaussian, stripe, impulse, dead-line, and mixed noise across different HSIs or spectra with one model.
  • SSGN uses spatial and adjacent spectral data in fully cascaded multi-scale convolutional blocks for HSI denoising.
  • Joint spatial and spectral gradients target sparse-noise directionality, complementary spectral information, and reduced spectral distortion.

1) Filter-Based Methods:

Filter-based HSI denoising methods separate clean signals from noisy signals through transformations or non-local filtering operations.

  • 1) Filter-Based Methods:: Filter-based methods use Fourier, wavelet, or non-local means filtering to separate clean signals from noisy HSI signals.One example applies spatial-spectral derivative-domain wavelet shrinkage to exploit differing signal properties across dimensions.

2) Model Optimization-Based Methods:

Model optimization-based methods incorporate HSI priors such as total variation, sparsity, and low-rank structure to restore spatial-spectral characteristics. The paper motivates SSGN as a data-driven response to limited adaptability and efficiency in hybrid-noise removal.

  • 2) Model Optimization-Based Methods:: High spectral correlation and within-band spatial similarity motivate low-rank matrix and tensor models for mixed-noise HSI restoration.
  • 2) Model Optimization-Based Methods:: The paper presents SSGN to address existing methods' limited adaptability to hybrid noise and low efficiency through a deep-convolutional, data-driven framework.

A. Holistic Framework Description

SSGN performs end-to-end residual-noise estimation from a noisy HSI band together with its spatial and adjacent spectral gradients. The model traverses the bands to support hybrid-noise reduction.

  • A. Holistic Framework Description: SSGN takes a noisy band, its horizontal and vertical spatial gradients, and adjacent spectral gradients as inputs, then outputs that band's residual noise.
  • A. Holistic Framework Description: The model learns end-to-end between noisy and clean HSI patches and applies the same procedure across all bands.

B. The Proposed SSGN Model for HSI Denoising

SSGN denoises HSIs by jointly learning spatial and spectral gradients within a cascaded multi-scale convolutional architecture. Its loss balances spatial reconstruction with spectral-gradient preservation.

  • Joint Spatial and Spectral Gradient Information: SSGN jointly uses each noisy band, its horizontal and vertical gradients, and adjacent spectral gradients to estimate residual noise.The final denoised band is reconstructed from the input band and the learned residual through cascaded feature transformations.
  • Joint Spatial and Spectral Gradient Information: Spatial gradients highlight the directional structure of sparse noise, while spectral differences provide complementary information because noise varies across HSI bands.The method uses these two gradient types together to address mixed noise.
  • Multi-Scale Convolutional Blocks: Multi-scale convolutional blocks use different receptive-field sizes to capture contextual structure and sparsely distributed stripes or dead lines.The blocks use 3 × 3, 5 × 5, and 7 × 7 convolutions for spatial and spectral data.
  • Multi-Scale Convolutional Blocks: Fully cascaded blocks progressively produce feature maps that approximate residual mixed noise, including dense Gaussian noise and sparse stripes or dead lines.The cascaded design extracts features at multiple depths and scales.
  • Spatial-Spectral Loss Function: The spatial-spectral loss combines spatial and spectral terms, with α controlling their trade-off during supervised training.The spectral term represents estimated spectral gradients of neighboring bands, while the spatial term uses the estimated residual output.

IV. EXPERIMENTS AND DISCUSSIONS

The experiments evaluate SSGN on simulated and real HSI data using established hybrid-noise baselines and multiple test datasets. The setup varies noise across bands and uses separate training and test imagery.

  • Experimental Setup: SSGN is compared with HSSNR, BM4D, LRMR, LRTV, and NonLRMA on simulated and real noisy HSI data.The compared methods represent hybrid spatial-spectral, block-matching, and low-rank denoising approaches.
  • Parameter Settings: The SSGN uses K = 24 adjacent spectral bands and α = 0.001 for both simulated and real-data experiments.The model is trained with Adam optimization, using momentum parameters of 0.9, 0.999, and 10^-8.
  • Network Training: Training uses University of Pavia and Washington DC Mall HSIs, cropped into 25 × 25 patches after removing noisy and water-absorption bands.Simulated patches combine AWGN, stripe noise, and dead lines with varying intensity and distribution across bands.
  • Test Data Sets: The experiments use four datasets spanning simulated and real-data evaluation, including Washington DC Mall, HYDICE Urban, AVIRIS Indian Pines, and EO-1 Hyperion.The datasets are cropped or filtered to remove severely degraded or water-absorption bands before evaluation.

A. Simulated-Data Experiments

Simulated experiments cover Gaussian, stripe, dead-line, and combined hybrid-noise cases across several signal-to-noise levels. SSGN achieves the strongest reported quantitative performance and preserves visual quality better than the compared methods.

  • Simulated Noise Cases: The simulated cases include Gaussian noise, stripe noise, Gaussian-plus-stripe noise, Gaussian-plus-dead-line noise, and all three noise types together.The combined case is evaluated at SNR levels of 8, 18, 28, and 38 dB.
  • Visual Comparison: Figures 6–8 compare pseudo-color or gray-scale denoising results for Cases 3, 4, and 5.1 across the six methods.The visual comparisons use selected bands, including bands 57, 27, and 17 for Case 3 and band 164 for Case 4.
  • Quantitative Results: SSGN achieves the highest MPSNR and MSSIM and the lowest MSA among the compared methods across all simulated cases.Table I reports the hybrid-noise quantitative comparison across the five simulated cases.
  • Visual Comparison: Compared with SSGN, competing methods retain residual noise, stripes, spectral distortion, or dead lines under complex mixed-noise conditions.BM4D also produces over-smoothing, while low-rank methods can leave artifacts in magnified regions.
  • Parameter Sensitivity Analysis: For mixed-noise cases, MPSNR peaks and MSA reaches its minimum at α = 0.001, whereas increasing α thereafter worsens spectral distortion.Under Gaussian-only noise, the spatial-only loss slightly outperforms the spatial-spectral loss in MPSNR.

B. Real-Data Experiments

Real-data experiments on Urban, Indian Pines, and Hyperion EO-1 images show that SSGN removes varied mixed noise while preserving spatial, structural, and spectral details better than comparison methods.

  • Real-data comparisons: SSGN outperforms the comparison methods on Urban, Indian Pines, and Hyperion EO-1 data by removing mixed noise while preserving local or structural details without obvious over-smoothing or spectral distortion.The comparisons cover dense, stripe, impulse, Gaussian, and dead-line corruption across the three real datasets.
  • HYDICE Urban Data Set: On Urban data, HSSNR leaves mixed noise, BM4D over-smooths, and LRMR, LRTV, and NonLRMA fail to preserve spectral information, whereas SSGN performs best in the image and DN-profile comparisons.The figure set includes band 104 denoising results and horizontal mean DN profiles.
  • AVIRIS Indian Pines Data Set: On Indian Pines, SSGN best suppresses dense and impulse noise while preserving high-frequency details and structural information across single-band and false-color results.The competing methods retain residual noise or stripes, or smooth and destroy details.
  • Hyperion EO-1 Data Set: On Hyperion EO-1, SSGN removes mixed noise and preserves local details and structural information, while other methods either over-smooth or fail to recover dead lines.The comparison uses band 2 images and vertical mean DN profiles.

C. Discussion

Discussion evaluates SSGN through classification accuracy, runtime, and overall comparisons, finding broad advantages across mixed-noise scenarios while identifying remaining scope limitations.

  • Classification validation: SSGN achieves the highest Indian Pines classification performance, with an overall accuracy of 85.4% and a kappa coefficient of 0.831.SVM is used under the same environment for all restoration results.
  • Run-time comparison: SSGN has the lowest runtime in the three real-data experiments under the reported computing environment.The paper attributes this efficiency to its unified learning framework operating in GPU mode.
  • Overall evaluation: SSGN outperforms existing HSI denoising algorithms in most evaluation indices, visual assessments, classification accuracy, and time consumption across simulated and actual mixed-noise experiments.The overall evaluation cites Tables I–III and Figs. 11–17 as evidence across multiple evaluation dimensions.
  • Overall evaluation: The method still has limitations for more complex dense-distributed strip noise and independent band normalization.These limitations are stated as remaining issues in the overall evaluation.

V. CONCLUSION

The conclusion presents SSGN as a spatial-spectral gradient network for reducing mixtures of Gaussian, stripe, impulse, and dead-line noise in HSIs, while identifying directions for future improvement.

  • V. CONCLUSION: SSGN is presented for hybrid HSI noise reduction covering Gaussian noise, stripe noise, impulse noise, dead lines, and their mixtures.Future work proposes incorporating additional HSI priors and developing holistic band normalization.
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