Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2014, Vol. 11, No. 2, pp. 9-17
Application of randomized principal component analysis for compression of hyperspectral data
S.I. Smirnov
1 , V.V. Mikhailov
1 , V.N. Ostrikov
1 1 Joint-Stock Company «Luch», branch in St.-Petersburg, Saint-Petersburg, Russia
The paper is devoted to issues related to compression of hyperspectral data. Among a number common methods, principal component analysis (PCA) is chosen because it allows to produce spectral identification of data in compressed space with economy of processing time because of much smaller dimension of this space. Moreover, this decreasing of computational costs is universal for wide class of spectral identification problems. However, the classical implementation of the PCA method has a relatively high computational complexity, in which the highest number of operations because of high spatial resolution of modern sensors is spent on the calculation of the covariance matrix. In this paper, methods for reducing the computational complexity via randomization are discussed.
In the literature, there are several approaches to this problem. Some authors suggest to use random sampling of hypercube pixels, some other - project an averaged cube to the space of lower dimension via Johnson - Lindenstrauss transform. Two these approaches are studied for implementation on hyperspectral data obtained from aircraft sensors. Both methods were tested on several sets of real data. A comparison of these approaches is given.
Keywords: PCA, compression, hyperspectral data, randomization,Johnson - Lindenstrauss transform
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