Denoising of hyperspectral imagery by cubic smoothing spline in the wavelet domain

The acquired hyperspectral images (HSIs) are inherently affected by noise with band-varying level, which cannot be removed easily by current approaches. In this study, a new denoising method is proposed for removing such kind of noise by smoothing spectral signals in the transformed multiscale domain. Specifically, the proposed method includes three procedures: 1) applying a discrete wavelet transform (DWT) to each band; 2) performing cubic spline smoothing on each noisy coefficient vector along the spectral axis; 3) reconstructing each band by an inverse DWT. In order to adapt to the band-varying noise statistics of HSIs, the noise covariance is estimated to control the smoothing degree at different spectral positions. Generalized cross validation (GCV) is employed to choose the smoothing parameter during the optimization. The experimental results on simulated and real HSIs demonstrate that the proposed method can be well adapted to band-varying noise statistics of noisy HSIs and also can well preserve the spectral and spatial features.