A comparative study of signal transformation techniques in automated spectral unmixing of infrared spectra for remote sensing applications

From geological and planetary exploration perspectives, automated sub-pixel classification of hyperspectral data is the most difficult task as it involves blind unmixing with library spectra of minerals. In this study, we demonstrate a procedure involving spectral transformation and linear unmixing to achieve the above task. For this purpose, infrared spectra of rocks from the spectral library, field, and remotely sensed hyperspectral image cube were used. Potential spectra of minerals for unmixing rock spectra were drawn from the library based on similarity of absorption features measured using Pearson correlation coefficient. Eight transformation techniques namely, first derivative, fast Fourier transform, discrete wavelet transform, Hilbert–Huang transform, crude low pass filter, S-transform, binary encoding, spectral effective peak matching, and two sparsity-based techniques (orthogonal matching pursuit, sparse unmixing via variable splitting, and augmented Lagrangian) were evaluated. Subsequently, minerals identified by above techniques were unmixed by linear mixture model (LMM) to decipher mineralogical composition and abundance. Results of LMM achieved using fully constrained least-square-estimation-based quadratic programming optimization approach were evaluated by conventional procedures such as X-ray diffraction and microscopy. In the case of image cube, endmembers derived using minimum noise fraction and pixel purity index were subjected to above procedure. It is evident that the discrete-wavelet-transformation-based approach produced excellent and meaningful results due to its flexibility in scaling the data and capability to handle noisy spectra. It is interesting to note that the adopted procedure could perform sub-pixel classification of image cube automatically and identify predominance of dolomite in limestone and sodium in alunite based on subtle differences in absorption positions.