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In this paper, we investigate the problem of signal subspace identification (SSI) and dimensionality reduction in hyperspectral images. We consider two recently proposed SSI algorithms: the Maximum Orthogonal Complement Analysis (MOCA) algorithm and the Robust Signal Subspace Estimator (RSSE) algorithm. Such algorithms are robust to the presence of rare signal components and are particularly effective in reducing the number of features in the preprocessing step for small target detection applications. In this paper, MOCA and RSSE are briefly revisited and integrated in a common theoretical framework in order to better highlight and understand their peculiarities. Furthermore, their performances are compared in terms of computational complexity and of their ability to address both the abundant and the rare signal components. A modified version of the MOCA is also introduced, which is computationally more efficient than the original algorithm. Results on simulated data are discussed, and a case study is presented concerning real Airborne Visible/Infrared Imaging Spectrometer data.