Space-adaptive spectral analysis of hyperspectral imagery

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 up a set of vectors fitting pixel spectra to the largest extent. A common technique to select the most representative elements of a signal is Matching Pursuit (MP). This technique is analogous to the Mixed-Transform Analysis (MTA) and has been successfully used to represent speech and images. The main problems in using MTA for hyperspectral data analysis are: (1) choice of bases that potentially convey the maximum of spectral information; (2) calculation of projections in the non-orthogonal representation. A large variety of bases has been taken into consideration, including several types of wavelets with compact support. An iterative approach is used to find the coefficients of the linear combination of vectors, so that the residual function has minimum energy. The computational cost is extremely high when a large set of data is to be processed. To encompass computational constraints, a reduced data set (RDS) is produced by applying the projection pursuit (PP) technique to each of the square blocks in which the input hyperspectral image is partitioned based on a spatial homogeneity criterion. Then MTA is applied to the RDS to find out a non-orthogonal frame capable to represent such data through waveforms selected to best match spectral features. Experimental results carried out on the hyperspectral data AVIRIS Moffett Field '97 show the joint use of different bases, including wavelet bases, may be preferable to a unique orthogonal basis in terms of energy compaction, as well as of significance of the outcome components.