Unbiasedness of regression wavelet analysis for progressive lossy-to-lossless coding

The recently proposed Regression Wavelet Analysis (RWA) scheme holds a great promise as a spectral transform for compressing hyperspectral images due to its low complexity, reversibility, and demonstrated superior coding performance. The scheme is based on a pyramidal prediction, using multiple regression analysis, to exploit statistical dependence in the wavelet domain. For lossless coding, RWA has proven to offer better performance than other spectral transforms like reversible PCA and also better than the best and most recent lossless coding standard in remote sensing, CCSDS-123.0. For progressive lossy-to-lossless coding, RWA also yields improved performance as compared to PCA. In this paper, we show that the RWA parameters are unbiased for lossy coding, where the regression models are used not with the original transformed components, but with the recovered ones, which lack some information due to the lossy reconstruction. As a byproduct, we also report that the Exogenous RWA model, a variant of RWA where the employed regression parameters have been trained using other images from the same sensor, still provides almost identical performance to that obtained by applying regression on the same image, thus showing that hyperspectral images with large sizes in the spectral dimension can be coded via RWA without side information and at a lower computational cost.