Dimensionality reduction of hyperspectral images using an ICA-based stochastic second-order optimization algorithm

Hyperspectral imaging is one of the advanced remote sensing techniques whose goal is to obtain the spectrum for each pixel in the image of a scene, with the purpose of finding objects, identifying materials or detecting processes. However, the high dimensional nature of hyperspectral images makes their analysis complex. Various methods have been developed to reduce the dimension of hyperspectral images. Most commonly used dimension reduction techniques are Principal Component Analysis (PCA) and Independent Component Analysis (ICA). PCA is a method to reduce the dimensionality by removing the correlation among the bands, while ICA finds additively independent components. FastICA is one of the most used ICA algorithms. It is based on maximizing a loss derived from the fourth order statistical moment (kurtosis) or negentropy, which are both non-convex functions. Moreover, FastICA can find irrelevant stationary points (no maxima) and is not scalable as it uses at each iteration the whole set of pixels. In this paper, we present a stochastic second-order Taylor-based algorithm adapted to such ICA non-convex loss functions. Our algorithm guarantees ascent, hence it usually identifies (local) maxima. Moreover, the algorithm since it is stochastic, is scalable. Detailed numerical simulations show the superior performance of our method compared to FastICA.