Research on Spectrum Denoising Methods Based on the Combination of Wavelet Package Transformation and Mathematical Morphology

The present study introduced the generalized morphological filter into the denoising of visible and near infrared spectra for the first time, and provided a new method for denoising the reflectance spectra by combining mathematical morphology methods with the wavelet packet transformation. The authors used vegetable spectra from USGS spectral library as the reference spectra, and obtained the noised spectra by adding noises with different signal-to-noise ratios to the referenced spectra. The results were evaluated by signal-to-noise ratio (SNR), root mean squared error (RMSE), normalized correlation coefficient (NCC) and smoothness ratio (SR) of the denoised spectra. The authors’ results showed that both the thresholding on wavelet packet decomposition best bases method and the generalized morphological filter method could maintain the spectral shape and the spectral smoothness after denoising. The generalized morphological filter method can remove larger amplitude random noise whereas the continuous small amplitude random noise could not be removed well. Hence, the denoised spectra were not smooth. Nevertheless, the denoised spectra using the thresholding on the best base groups of wavelet packet decomposition method were smooth, but the larger amplitude noise could not be removed completely. The authors’ method by combining the two methods has the merits of the two methods but removing their defects. The results showed that both large and small amplitude noise could be removed completely, meanwhile the normalized correlation coefficient (NCC) and smoothness ratio (SR) were improved, which indicated that the authors’ method is superior to other methods in denoising visible and near infrared spectra.