Typical Application of Graph Signal Processing in Hyperspectral Image Processing
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摘要: 高光谱图像(HSI)具有纳米级的光谱分辨能力且同时对地物目标的光谱维和空间维进行联合成像的优势，能够精细化感知场景目标的本征判别属性，在遥感探测、医疗诊断和国防安全等具有重要应用价值，是高精度遥感探测的科技制高点之一。不同于传统1维时间信号、2维图像信号，高光谱图像具有多阶、高维的信号属性。为解决传统信号处理方法在高光谱图像处理领域中的不足，图信号处理(GSP)理论与方法被逐渐引入高光谱图像处理与解译等任务中。该文以短综述的形式，介绍了图信号处理在高光谱图像处理领域的理论发展并列举了在高光谱特征提取、图像重构和解译分类3个主要方面的典型应用。最后，进一步探讨了该方向未来发展所面临的挑战和相应解决办法。Abstract: HyperSpectral Image(HSI) has nanometer-level spectral discriminative ability, capturing the spectral and spatial information of the ground objects simultaneously, within the integration of three-dimensional image cube. The capability to finely sense the intrinsic properties of objects makes it universally applied to many fields, e.g., remote sensing & detection, medical imaging & diagnosis, military defense & security, etc. Different from traditional one-dimensional time-series signals and two-dimensional image signals, HSIs are third-order tensor signals, with the spectral bands in the third-mode being high-dimensional. To eliminate the deficiencies of existing techniques in solving HSI processing and interpretation problems, Graph Signal Processing (GSP) is introduced. A short overview of the theoretical and technological development of GSP is given, along with its typical applications in HSI feature extraction, restoration, and classification. Based on the survey of the existing research basis, the future challenges and potential approaches to solve them in the community are also pointed out and discussed.
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算法1 基于SLRG的有监督高光谱特征提取算法 (1) 输入${\boldsymbol{X}}$，特征提取维数$ k $ (2) for $ i = 1:C $ do (3) for $ j{\text{ = 1}}:{c_i} $($ {c_i} $表示第$ i $类样本个数) do (4) 根据式(9)对每个${\boldsymbol{x}}_j^{(i)}$用其同一类别的训练数据求稀疏
低秩表示系数${\boldsymbol{w} }_j^{(i)}$(5) 同一类别的稀疏低秩表示矩阵${{\boldsymbol{W}}^{(i)} } = [{{\boldsymbol{W}}^{(i)} };{\boldsymbol{w}}_j^{(i)}]$ (6) end for (7) 构建稀疏低秩表示图${\boldsymbol{W} } = {\text{diag} }({ {\boldsymbol{W} }^{(1)} },{ {\boldsymbol{W} }^{(2)} }, \cdots ,{ {\boldsymbol{W} }^{(C)} })$ (8) end for (9) 根据式(10)求得${\boldsymbol{P}}$ (10) 输出${\boldsymbol{Y}} = {{\boldsymbol{P}}^{\text{T} } }{\boldsymbol{X}}$ 
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