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Orthogonal subspace projection (OSP) is a powerful tool for dimensionality reduction (DR) in hyperspectral images (HSIs). In the OSP approach, the basis of the signal subspace must be estimated from the data themselves. Such estimation task is referred to as signal subspace identification (SSI). Most of the SSI methods in the literature are based on the analysis of the data second-order statistics (SOS) and have two main drawbacks: 1) They do not take into account the rare signal components (or rare vectors), 2) they assume that noise is spatially stationary. Rare vectors are those signal components that are present in pixels scarcely represented in the image and linearly independent on the signal components characterizing the rest of the image pixels. SOS-based SSI algorithms estimate the signal subspace addressing mostly the background and ignoring the presence of the rare pixels. This may be detrimental for the performance of detection algorithms when DR is adopted as a pre-processing step in small target detection applications. In this paper, a new technique for SSI in HSIs is presented. The algorithm is developed to account for both the abundant and the rare signal components. The method is derived by assuming a signal-dependent model for the noise affecting the data. This makes the SSI algorithm particularly suitable for the processing of images acquired by new generation sensors where, due to the improved sensitivity of the electronic components, noise includes a signal-dependent term. Results on simulated data are discussed, and the comparison with a recently proposed technique based on the analysis of SOS is performed. Furthermore, the results obtained by applying the SSI algorithm to a real HSI affected by signal-dependent noise are presented and discussed.