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纸质出版日期： 2023-08-16 ，
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龙珍， 刘翼鹏， 苟艺馨， 曾思行， 刘佳妮， 文飞， 朱策. 2023. 高光谱图像的线性张量子空间模型及降噪应用. 中国图象图形学报， 28(08):2505-2521
Long Zhen， Liu Yipeng， Gou Yixin， Zeng Sixing， Liu Jiani， Wen Fei， Zhu Ce. 2023. Linear tensor subapace model based hyperspectral image denoising. Journal of Image and Graphics， 28(08):2505-2521
目的
2
与标准RGB图像相比，高光谱图像（hyperspectral image，HSI）具有更为精细的光谱划分，这一特点可以为后续的图像分析处理带来更好的性能。然而在采集过程中，HSI可能会受到严重的噪声污染，比如高斯噪声、脉冲噪声、条纹噪声和死线噪声。受到污染的HSI在一定程度上会影响后续分析算法的性能，因此在进行图像分析处理之前，对采集到的HSI进行降噪是非常重要的。
方法
2
为了得到干净的HSI，本文提出了一种新的结构型张量分解算法，并将其应用于HSI降噪。该算法根据HSI的线性子空间模型，将干净的高光谱图像分解为矩阵向量外积的和，其中向量表示光谱的正交基，矩阵表示基对应的系数，即特征图像。考虑特征图像的低秩性，矩阵核范数算子被直接施加在特征图像上，这样既可以充分探索高光谱图像的全局信息，又可以避免对原始张量进行低秩约束所带来的计算负担。
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-范数和F-范数（Frobenius norm）最小化算子分别用来去除脉冲噪声、死线和条纹在内的稀疏噪声和一些现实场景中的高斯噪声。此外，为了提升图像恢复的质量，添加了各向异性全变分算子来探索高光谱图像的空间局部平滑属性。经典的交替方向乘子法用于求解所提出的低秩降噪模型。
结果
2
在2个模拟数据集和2个真实数据集上与最新的7种方法进行对比，其中，在具有脉冲噪声的模拟数据上，尤其在实验3和实验4的噪声环境下，相比于性能第2的模型，平均峰值信噪比增加了2.1 dB，无量纲全局相对综合误差降低了15.5%。同时，真实数据集中，在数据具有高斯、条纹和死线噪声的情况下，提出的降噪算法提高了HSI的空间分辨率。
结论
2
本文提出的HSI降噪模型考虑了HSI的线性张量子空间模型，在处理混合噪声时恢复性能更好，因此在应用于较为复杂的场景时具有显著优势。
Objective
2
Spectrometers-based hyperspectral imaging technique is focused on multi-spectral bands data collection in the same region， e.g.， ranging from 400 nm to 2 500 nm. Targets information is beneficial from both spectral and spatial information in terms of spectral bands-derived multiple and consistent features. Compared to such standardized RGB image， hyperspectral image （HSI） is capable for some image-contexual applications like remote sensing， food safety and medical diagnosis. However， due to thermal electronics， dark current， and random error of light count are challenged to be resolved for image processing， the obtained HSI is inevitably affected by such severe noise， including Gaussian noise， impulse noise， dead lines and stripes. It will definitely degrade image quality and hinder its subsequent applications. As a result， HSI-derived noise removal has emerged and developed to deal with that. Currrent HSI denoising algorithms can be segmented into two categories： one category is concerned about data-driven contexts and the other one is focused on model-driven contexts. Data-driven deep learning technique is beneficial for HSI denoising. For model-based aspect， low-rank approximation performs well without training. Low-rank based denoising methods can be divided into matrix- and tensor-based contexts. The matrix-based denoising methods can be used to unfold the three-dimensional tensor into a matrix or treat each band solely. These two-dimensional denoising algorithms are challenged to achieve optimal results since the joint spatial-spectral information of HSI is distorted partially. To resolve this problem， the low-rank tensor recovery uses both the spectral and spatial information of the HSI， and it can achieve better results than the low rank matrix recovery methods to some extent. However， existing tensor-based methods like CP-based or Tucker-based ones are used to treat HSI as a 3rd-order image only， and image-prior information is required to be taken into account for processing. Actually， the HSI has its own prior information beyond image attributes. For example， spectral vectors are linked to a low-dimensional linear subspace in this manner and its corresponding coefficient matrix has a low rank structure.
Method
2
We develop an orthogonal vectors-based structural low rank matrix-vector tensor factorization （MVTF）. It decouples an HSI into a sum of outer matrix-vector products， where the vectors are orthogonal bases and matrices are the corresponding coefficients， called eigen-images. Due to the low-rank structure of eigen-images is existed， nuclear norm minimization operators are penertrated into the matrices straighforward， and the global spatial-spectral information of HSI can be well extracted. Additionally， the anisotropic total variation is used for spatial piecewise smoothness farther. Furthermore， sparse noise is composed of impulse noise， dead lines and stripes， and it is detected by the
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-norm regularization. The Frobenius norm is used to the heavy Gaussian noise for natural-based scenarios. The alternating direction method of multipliers is adopted to resolve the proposed optimization model， which can mine the global low-rank spatial-spectral property and the spatial smoothness of the HSI simultaneously.
Result
2
The comparative analysis is carried out in relevance to seven popular ones on 2 kind of simulated datasets of Washington DC Mall （WDC） and Pavia University （PaviaU）， and such 2 sort of real datasets of EO-1 Hyperion datasets （EO-1） and HYDICE Urban Dataset （Urban）. To evaluate the performance quantitatively， four metrics are used to evaluate the image denoising quality， including mean peak signal to noise ratio （MPSNR， e.g.， larger is better）， mean structural similarity index （MSSIM， e.g.， larger is better） and dimensionless global relative error of synthesis （ERGAS， e.g.， less is better） and CPU processing time. To verify the effectives of proposed method， Gaussian noise， salt-and-pepper （impulse） noise， dead line and strip noise are added into ground-truth datasets simulation as well. In detail， MPSNR can be increased by 1.6 dB， and ERGAS is decreased by 14% in case 1. This means that our algorithm has its potential to remove Gaussian and impulse noise. Similarly， in cases 3 and 4 with dead line and stripe noise， MPSNR can be increased by 2.1 dB and 1.5 dB， and ERGAS is decreased by 15.5% and 24.5%. But， in case 2 only with Gaussian noise and dead lines， nonlocal-similarity based methods are developed with sacrifice of CPU running time-related computational complexity. To validate the optimization further， we add two cases for comparison with only Gaussian noise or impulse noise， where the variance of Gaussian noise is 0.15 and the percentage of impulse noise is 0.2. For PaciaU and WDC data， nonlocal-similarity based methods， and our proposed one are used for this. The experimental results show that nonlocal-similarity-based methods perform well on Gaussian noise， while our proposed method can optimize impulse noise. It implies that a nonlocal-similarity prior is appropriated for the removal of Gaussian noise， even if impulse noise has been considered in the denoised optimization model. Additionally， for the real data denoising experiments， there are some actual bands in EO-1 and Urban datasets that have been more contaminated in related to the Gaussian noise， stripes， and dead lines. Experimental results on EO-1 hyperspectral image demonstrate that our proposed algorithm can recover the HSI while preserving the HSI’s local details and structural information. For Urban datasets in related to severe Gaussian noise， stripe noise， and dead line， the proposed method is beneficial to recover a clean image under severely noisy circumstances.
Conclusion
2
A newly structured low rank MVTF model is facilitated， for which the linear subspace model of HSI can be developed for HSI denoising. The proposed denoising method is beneficial to deal with the mixed noisy condition in terms of its potentials for HIS-related latent information. Furthermore， the proposed structural tensor decomposition is predicted that it is suitable for a series of HSI’s applications like HSI unmixing and HSI fusion to a certain extent.
高光谱图像（HSI）图像降噪矩阵向量张量分解（MVTF）全变分（TV）线性子空间模型
hyperspectral imaging（HSI）image denoising（TV）matrix-vector tensor factorization（MVTF）total variationlinear subspace model
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