Matching pursuit 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 the subset of such vectors best matching pixel spectra. A common technique to select the most representative elements of a signal is Matching Pursuit (MP). 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. Therefore, a reduced data set (RDS) is produced by applying the projection pursuit (PP) technique to each of the segments in which the hyperspectral image is partitioned based on a spatial homogeneity criterion of pixel spectra. Then MP is applied to the RDS to find 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 compare a dictionary of wavelet functions with a dictionary of endmembers spectra. Although the former is preferable in terms of energy compaction, the latter is superior for physical significance of the resulting components.