Hyperspectral data analysis by mixed transforms

Aim of this paper is investigating the use of overcomplete bases for the representation of hyperspectral image data. The idea is building an overcomplete basis starting from several orthogonal or non-orthogonal bases and picking a set of vectors fitting pixel spectra to the largest extent. This technique, denoted also as Mixed-Transform Analysis (MTA), has been successfully used to represent speech and images. The main problems in using MTA for hyperspectral data analysis are: (1) choice of bases (at least two) that potentially convey maximum spectral information; (2) computation of projections in the non-orthogonal representation. Selection of vectors from the overcomplete basis can be made in different ways. A large variety of bases has been taken into consideration, including several type of wavelets with compact support. Representation of data as a linear combination of the selected basis vector is complicated by the fact that these vectors are non-orthogonal. The computational cost is extremely high when a large set of data is to be processed. For these reasons, an iterative approach is used to find the coefficients of the linear combination of vectors, so that the residual function has minimum energy. Experimental results carried out on hyperspectral data collected in AVIRIS Moffett Field '97 show the joint use of two different bases, possibly including a wavelet, is preferable to a unique orthogonal basis in terms of energy compaction, as well as of significance of the outcome components.