On the suitability of using the residual method for estimation of the noise covariance matrix in hyperspectral images

Hyperspectral images (HSI) have found widespread application in many disciplines because of their ability to characterize the object being imaged in a much more detailed manner as compared to colored or multispectral images. An accurate modelling of the underlying noise is, however, necessary in order to extract the useful data from the HSI. Although, classically noise in HSI has been modelled as independent of the signal, and spatially and spectrally uncorrelated, recent studies have shown the signal dependence of the noise as well as the presence of spectral correlation in the noise. In this work, we focus on the spectral correlation characteristic of noise in hyperspectral images. We make use of the multiple regression/residual method and provide an accurate analytical model for representation of noise variances and noise spectral covariances in terms of the residuals. We test the suitability of the classic residual model as well as our proposed analytical model for both artificially created and real datasets and show that the classic residual method does not provide an accurate model for the estimation of the noise covariance matrix.