Band Selection for Hyperspectral Images Using Non-Negativity Constraints

Abstract

This paper presents a new factorization technique for hyperspectral signal processing based on a constrainedsingular value decomposition (SVD) approach. Hyperpectral images typically have a large number of contiguous bands thatare highly correlated. Likewise the field of view typically contains a limited number of materials and the spectra are alsocorrelated. Only a selected number of bands, the extreme bands that include the dominant materials spectral signatures,are needed to express the data. Factorization can provide a means for interpretation and compression of the spectral data.Hyperspectral images are represented as non-negative matrices by graphic concatenation, with the pixels arranged intocolumns and each row corresponding to a spectral band. SVD and principal component analysis enjoy a broad range ofapplications, including, rank estimation, noise reduction, classification and compression, with the resulting singular vectorsforming orthogonal basis sets for subspace projection techniques. A key property of non-negative matrices is that theircolumns/rows form non-negative cones, with any non-negative linear combination of the columns/rows belonging to thecone. Data sets of spectral images and time series reside in non-negative orthants and while subspaces spanned by SVDinclude all orthants, SVD projections can be constrained to the non-negative orthants. In this paper we utilize constraintsets that confine projections of SVD singular vectors to lie within the cones formed by the spectral data. The extremevectors of the cone are found and these vectors form a basis for the factorization of the data. The approach is illustratedin an application to hyperspectral data of a mining area collected by an airborne sensor.