CAJ | 학술논문

光谱微分技术在高光谱数据处理中应用广泛，为研究分数阶微分对光谱反射率与盐渍土含盐量之间相关系数的影响，细化相关系数变化趋势，该文选取新疆塔里木南缘于田绿洲盐渍土为研究对象，以土壤样本含盐量和反射率高光谱数据为数据源，利用Grünwald-Letnikov分数阶微分公式编程计算光谱反射率以及对应的均方根、倒数、对数、对数倒数、倒数对数变换的0～2阶微分（间隔0.2阶），对比分析每种变换各阶微分与土壤含盐量相关系数曲线的变化趋势以及微分处理对单波段相关系数的影响。结果表明：经微分处理，通过相关系数0.01显著性检验水平的波段数量明显增加（0.6阶＞1阶＞2阶＞0阶），随着阶数增加，呈现先增后减的趋势，且均在分数阶0.6处达到最多。在0.6阶处，光谱反射率及5种数学变换通过相关系数0.01显著性检验的波段数量按照从大到小为：倒数对数变换=对数变换＞均方根变换＞倒数变换＞光谱反射率＞对数倒数变换。对于波段2444、2423、2142、2005 nm，微分算法能够大幅提升与含盐量之间的相关性，相关系数绝对值取最大值对应的阶数均为分数阶。从局部到整体，分数阶微分提升相关性的效果明显优于整数阶微分。该研究结果为分数阶微分在高光谱技术监测土壤盐渍化现象中的应用提供参考依据。
광보미분기술재고광보수거처리중응용엄범，위연구분수계미분대광보반사솔여염지토함염량지간상관계수적영향，세화상관계수변화추세，해문선취신강탑리목남연우전록주염지토위연구대상，이토양양본함염량화반사솔고광보수거위수거원，이용Grünwald-Letnikov분수계미분공식편정계산광보반사솔이급대응적균방근、도수、대수、대수도수、도수대수변환적0～2계미분（간격0.2계），대비분석매충변환각계미분여토양함염량상관계수곡선적변화추세이급미분처리대단파단상관계수적영향。결과표명：경미분처리，통과상관계수0.01현저성검험수평적파단수량명현증가（0.6계＞1계＞2계＞0계），수착계수증가，정현선증후감적추세，차균재분수계0.6처체도최다。재0.6계처，광보반사솔급5충수학변환통과상관계수0.01현저성검험적파단수량안조종대도소위：도수대수변환=대수변환＞균방근변환＞도수변환＞광보반사솔＞대수도수변환。대우파단2444、2423、2142、2005 nm，미분산법능구대폭제승여함염량지간적상관성，상관계수절대치취최대치대응적계수균위분수계。종국부도정체，분수계미분제승상관성적효과명현우우정수계미분。해연구결과위분수계미분재고광보기술감측토양염지화현상중적응용제공삼고의거。
Soil salinization is not only one of the most serious environmental problems in semi-arid and arid area, but it also leads to land degradation and productivity loss. At present, most studies on soil salinization pay much attention to the quantifying of the relationship between the saline soil salt content and integer differential transform of hyperspectral data. The integer differential method only focuses on the points in differential windows, thus if extending the integer calculus to fractional order, more information could be discovered due to the advantages of fractional differential method: it has memory and nonlocality. In this paper, the authors took the Delta oasis of Yutian in the southern rim of Tarim Basin in Xinjiang as the study area, and measured the spectral reflectance and the soil salt content in order to obtain the degrees of salinity in the study area. Firstly, the hyperspectral reflectance data were treated with 5 kinds of mathematical transform:root mean square, inversion, logarithm, inversion-logarithm, and logarithm-inversion. Secondly we calculated their 0-2nd order (interval 0.2-order) derivative by using the Grünwald-Letnikov fractional order differential formula and Java programming language, then computed the correlation coefficient between the salt content and the data of each mathematical transform and each order differential. Subsequently, we comparatively analyzed the varying trend between correlation coefficient curves and the influence of correlation coefficient on single bands treated by the differential method. The results showed that differentials could evidently increase the number of the bands highly significantly correlated with salt content (0.6-order>first-order>second-order>0-order), the number followed increasing-decreasing trend (reaching the maximum at 0.6-order) with the increase of differential order. For spectral reflectance and other mathematical transform at 0.6-order, the numbers of the bands followed the order inversion-logarithm=logarithm>root mean square>inversion>spectral reflectance>logarithm-inversion. For the bands 2 444, 2 423, 2 142, and 2 005 nm, differential algorithm could significantly improve the correlation between salt content and spectra (and other mathematical transforms) of salinized soil, and all the maximum absolute values of correlation coefficient were obtained at the fractional order, corresponding to 0.6-order (logarithm-inversion transform corresponding to 0.4-order), 0.6-order (inversion transform corresponding to 0.8-order), 0.8-order, and 1.4-order respectively. In conclusion, from local to global, fractional differential had a better capacity than integer differential in lifting correlation. As the order increased, the correlation coefficient curves showed a gradual changing trend, and to some extent, capturing this trend could prevent information loss caused by big differences among the spectral reflectance, first-order, and second-order differential transform. We suggest here that further researches should be concentrated on physical meaning of fractional differential in hyperspectral data to provide theoretical basis to build and describe soil salinization quantitative inversion models.