Penalized Linear Discriminant Analysis of Hyperspectral Imagery for Noise Removal

The existence of noise in hyperspectral imagery (HSI) seriously affects image quality. Noise removal is one of the most important and challenging tasks to complete before hyperspectral information extraction. Though many advances have been made in alleviating the effect of noise, problems, including a high correlation among bands and predefined structure of noise covariance, still prevent us from the effective implementation of hyperspectral denoising. In this letter, a new algorithm named the penalized linear discriminant analysis (PLDA) and noise adjusted principal components transformation (NAPCT) was proposed. PLDA was applied to search for the best noise covariance structure, while the NAPCT was employed to remove the noise. The results of the tests with both HJ-1A HSI and EO-1 Hyperion showed that the proposed PLDA-NAPCT method could remove the noise effectively and that it could preserve the spectral fidelity of the restored hyperspectral images. Specifically, the recovered spectral curves using the proposed method are visually more similar to the original image compared with the control methods; quantitative matrices, including the noise reduction ration and mean relative deviation, also showed that the PLDA-NAPCT produced less bias than the control methods. Furthermore, the PLDA-NAPCT method is sensor-independent, and it could be easily adapted for removing the noise from different sensors.