A Supervised Method for Nonlinear Hyperspectral Unmixing

Due to the complex interaction of light with the Earth’s surface, reflectance spectra can be described as highly nonlinear mixtures of the reflectances of the material constituents occurring in a given resolution cell of hyperspectral data. Our aim is to estimate the fractional abundance maps of the materials from the nonlinear hyperspectral data. The main disadvantage of using nonlinear mixing models is that the model parameters are not properly interpretable in terms of fractional abundances. Moreover, not all spectra of a hyperspectral dataset necessarily follow the same particular mixing model. In this work, we present a supervised method for nonlinear spectral unmixing. The method learns a mapping from a true hyperspectral dataset to corresponding linear spectra, composed of the same fractional abundances. A simple linear unmixing then reveals the fractional abundances. To learn this mapping, ground truth information is required, in the form of actual spectra and corresponding fractional abundances, along with spectra of the pure materials, obtained from a spectral library or available in the dataset. Three methods are presented for learning nonlinear mapping, based on Gaussian processes, kernel ridge regression, and feedforward neural networks. Experimental results conducted on an artificial dataset, a data set obtained by ray tracing, and a drill core hyperspectral dataset shows that this novel methodology is very promising.

Nonlinear Blind Source Separation and Fault Feature Extraction Method for Mining Machine Diagnosis

Mining machines are strongly nonlinear systems, and their transmission vibration signals are nonlinear mixtures of different kinds of vibration sources. In addition, vibration signals measured by the accelerometer are contaminated by noise. As a result, it is inefficient and ineffective for the blind source separation (BSS) algorithm to separate the critical independent sources associated with the transmission fault vibrations. For this reason, a new method based on wavelet de-noising and nonlinear independent component analysis (ICA) is presented in this paper to tackle the nonlinear BSS problem with additive noise. The wavelet de-noising approach was first employed to eliminate the influence of the additive noise in the BSS procedure. Then, the radial basis function (RBF) neural network combined with the linear ICA was applied to the de-noised vibration signals. Vibration sources involved with the machine faults were separated. Subsequently, wavelet package decomposition (WPD) was used to extract distinct fault features from the source signals. Lastly, an RBF classifier was used to recognize the fault patterns. Field data acquired from a mining machine was used to evaluate and validate the proposed diagnostic method. The experimental analysis results show that critical fault vibration source component can be separated by the proposed method, and the fault detection rate is superior to the linear ICA based approaches.