Adaptive linear minimum mean square error restoration: influence on hyperspectral detection strategy

In this paper, we consider the problem of multichannel restoration. Current multichannel least squares restoration filters assume the separability of the signal covariance, which describes the between‐channel and within‐channel relationships. We propose a new solution for a multichannel restoration scheme, the Adaptive Linear Minimum Mean Square Error (ALMMSE), based on a local signal model, without the hypothesis of spectral and spatial separability. The proposed filter is developed to be used as a preprocessing step for detection in hyperspectral imagery. Tests on real data show that the proposed filter enables us to enhance detection performance in target detection and anomaly detection applications with the well‐known hyperspectral imagery detection algorithms AMF and RX. The comparison with detection results, after classical restoration methods, shows the superiority of the proposed approach for hyperspectral images.