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Robust Target Detection by Spatial/Spectral Restoration Based on Tensor Modelling

Target detection in hyperspectral images (HSI) in one of the most common applications. But the classical detection algorithms are sensitive to noise. It is crucial to well restore the spectral signature in order to decrease the noise dependence of the detection algorithm. In this paper, we propose a restoration method which takes advantage of spatial and spectral information in order to estimate the spectral signature without impair the discriminate power. Our method is based on tensor decomposition where all ways are processed simultaneously. By considering the cross-dependency of spatial and spectral information for the filtering, we improve the probability of detection. Our optimization criterion is the minimization of the mean square error between the estimated and the desired tensors. This minimization leads to estimate the n-mode filter for each way and are jointly estimated by using an Alternating Least Squares (ALS) algorithm. Comparative studies with the classical bidimensional restoration methods show that our algorithm exhibits better detection probability in noisy situation. Indeed, the detection probability obtained after our algorithm is higher than 0.7 until a signal to noise ratio equal to -3 dB.