光谱二值和多值编码技术能够实现目标光谱的快速匹配、 识别和分类等应用, 但这类量化编码方法会损失大量的光谱细节信息, 且不能解码出与原始光谱近似的重构光谱, 应用有限。 为了解决上述问题, 提出一种高阶残差量化的光谱编码新方法HOBC(high-order binary coding)。 首先, 对光谱向量进行去均值的规范化处理, 得到值域为(-1, 1)的光谱序列; 然后, 求解规范化光谱的±1编码、 编码系数和残差(即一阶残差); 基于一阶残差, 逐阶解算2至K阶残差的±1编码及其系数; 最后得到K个编码序列及其系数, 即为HOBC的编码结果。 选择典型波谱库数据集, 对比光谱0/1二值编码BC01(binary coding with 0 and 1)、 光谱分析编码SPAM(spectral analysis manager)、 二值/四值混合编码SDFC(spectral derivative feature coding)和DNA四值编码等4种方法, 进行了光谱量化编码和解码重构实验, 分别统计了光谱形状特征和斜率特征编码的信息熵和存储量、 光谱形状特征编码与原始光谱之间的光谱矢量距离SVD (spectral vector distance)、 谱间Pearson相关系数SCC (spectral correlation coefficient)和光谱角SAM (spectral angle mapping)。 结果表明, 在编码存储量上, HOBC的1～4阶编码分别与以上4种编码相等; 在编码信息熵上, HOBC的1～2阶编码分别与BC01和SPAM相等, 而HOBC的3～4阶编码分别高于SDFC和DNA编码; 在SCC上, HOBC1阶编码与BC01相等, 而2～4阶编码均分别优于SPAM, SDFC和DNA编码; 在SAM方面, HOBC 1～4阶编码均分别明显优于4种对比方法; 4种对比方法不能明确解码重构, 而HOBC可简便重构出与原始光谱近似的解码序列, 且SVD逐阶递减。 进一步, 基于临泽草地试验站公开光谱数据集, 进行了10类地物目标的光谱编码和监督分类实验, 实验结果表明, 在Kappa系数, 总体分类精度和平均分类精度等3种性能评价指标上, HOBC均明显优于4种对比方法, 尤其是, HOBC 4阶编码优于原始光谱的分类性能; 对样本数量较少且类间相似性较高的难分类地物, HOBC亦具有优于其他算法的鲁棒性。 说明HOBC编码在大幅压缩数据量的同时, 其编码序列能保留较高的信息量, 且具有较高的光谱可分性, 可用于光谱高精度快速识别和分类; 其解码重构序列与原始光谱序列具有较高的相似性, 理论上可适用于目标识别和分类等应用。

Spectral binary coding and multivalued coding technology can make objects spectra match, identify, and classify fast; but this kind of quantization coding methods will lose a lot of spectral details, and they cannot decode the reconstructed spectra similar to the original spectra. So they were only used for coarse horizontal applications in the past, such as rough classification. For resolving the above problems, a new spectral coding method, namely, HOBC (High-Order Binary Coding) was proposed based on high-order residual quantization. First, the original spectra were standardized by subtracting their own vector-mean, and thus the spectral sequences with a range of (-1, 1) were obtained. Second, the code with -1 and 1, its coding coefficient, and the residual (i. e., the first order residual) of a normalized spectrum were computed. Third, the binary codes with ±1 and their coding coefficients of the residuals from Two-Order to K-Order were computed order by order. At last, the K coding sequences and their corresponding coefficients were obtained. Using a typical spectral library dataset, spectral quantization encoding and decoding reconstruction experiments were carried out, compared with BC01 (spectral Binary Coding with 0 and 1), SPAM (SPectral Analysis Manager), a binary/quaternary hybrid coding, namely SDFC (Spectral Derivative Feature Coding), and a quaternary coding, namely DNA. During the experiments, first, the information entropy and memory storage of spectral shape feature and slope feature were calculated, respectively. Second, the spectral vector distance (SVD), spectral correlation coefficient (SCC), and spectral angle mapping (SAM) between the spectral shape feature and the original spectrum were calculated. The results of above experiments demonstrate that, on coding memory storage, HOBC 1—4 order encodings are equal to BC01, SPAM, SDFC, and DNA, respectively; on coding information entropy, HOBC 1—2 order encodings are equal to BC01 and SPAM, respectively, but HOBC 3—4 order encodings are higher than SDFC and DNA, respectively; on SCC, HOBC one order encoding is equal to BC01, but HOBC 2—4 order encodings are better than SPAM, SDFC, and DNA, respectively; on SAM, HOBC 1—4 order encodings are superior to the above four methods obviously, respectively; the four methods cannot be explicitly decoded and reconstructed, but it is easy to reconstruct the decoding sequence similar to the original spectrum for HOBC, and the SVDs of the reconstruct spectra are diminishing from a lower order to a higher order. Furthermore, the spectral coding and supervised classification experiments of 10 types of ground objects were carried out on the open spectral dataset of the Linze grassland foci experimental area. Results show that, on the three performance evaluation indices, i. e., Kappa value, overall classification accuracy, and average classification accuracy, HOBC is superior to the four coding methods. Especially, the classification performance of HOBC 4-order encoding is better than that of the original spectra. For the objects difficult to classify with small-sample and high similarity between classes, HOBC is also superior to other methods, and it is more robust. Therefore, first, HOBC can dramatically compress data. Meanwhile, its coding sequence can retain more information and have higher spectral separability, which can be used for fast identification and classification of spectra with high accuracy. At last, its decoding reconstruct data can also be used for the applications of target recognition and classification etc., theoretically, for the high similarity between the reconstruction spectra and original spectra.