针对单一分形维数在高光谱数据处理中的不足,提出了一种基于多重分形谱的光谱信号奇异性特征提取方法,引入多重分形谱表征光谱曲线的奇异性特征。该方法根据分形测度将光谱曲线进行划分,用光谱概率测度计算配分函数,通过尺度指数的Legendre变换实现光谱曲线多重分形谱的提取,根据各类地物间的类别可分性准则Bhattacharyya距离选择有效特征,最后利用地物分类实验来验证该方法的有效性。实验结果表明,多重分形谱用于分类时分类精度达95.2%,当其维数为原数据波段数的10%时,总体分类精度仍可达82.2%。多重分形谱表征了具有相同奇异性的波段子集的分形维数,准确的描述了光谱曲线的奇异性和分布特点,该方法能够有效地实现高光谱数据的特征提取。

Considering the fractal dimension deficiency to process hyperspectral data, a singularity feature extraction method was proposed, and the multifractal spectrum was used to characterize the singularity feature of spectra. In this method, the spectral curves were divided to several segments according to fractal measure, and the partition function was generated with the spectral probability measure. The multifractal spectrum was extracted with the Legendre transformation of scale exponent. Effective features of multifractal spectrum were selected based on discriminable rule of Bhattacharyya distance. Classification experiments of hyperspectral data are carried out to prove the value of multifractal spectrum, and the classification accuracy reaches 95.2%. With 10% of the original spectra’s dimension, the accuracy reaches 82.2%. The fractal dimension of spectral subset with the same singularity exponent is characterized by multifractal spectrum, and the singularity distribution of spectra are is expressed sufficiently. As a conclusion, the method is appropriate to extract the features of hyperspectral data.