A New Algorithm for Robust Estimation of the Signal Subspace in Hyperspectral Images in the Presence of Rare Signal Components

Abstract

This paper deals with the problem of signal subspace estimation for dimensionality reduction (DR) in hyperspectral images in the presence of rare pixels, i.e., pixels that are scarcely represented in the image and containing spectral components that are linearly independent of the background. Most of the classical methods proposed in the literature are based on the analysis of second-order statistics (SOS), which are weakly influenced by the rare signals. Therefore, such techniques estimate the signal subspace addressing mostly the background and ignoring the presence of rare pixels. This may reduce the target/background spectral contrast, thus decreasing the detection performance when DR is adopted as preprocessing task in small-target detection applications. In this paper, a new robust algorithm, namely, robust signal subspace estimation (RSSE), is developed, which preserves both abundant and rare signal components. It combines the analysis of SOS and a recent approach based on the analysis of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> norm. The novel contribution of this paper is twofold. First, the RSSE algorithm is presented, which includes a new iterative procedure to derive the signal subspace and an original statistical method to estimate the data dimensionality. Second, an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> simulation strategy is proposed to assess the performance of signal subspace estimation methods in the presence of rare signal components. The procedure is adopted to compare the RSSE algorithm with a classical technique based on the analysis of SOS. The results obtained by applying the two methods on a real Airborne Visible Infrared Imaging Spectrometer hyperspectral image are also presented and discussed.