A wavelet-based PCA reduction for hyperspectral imagery

Hyperspectral Imagery can provide very rich information on land cover classes. However, it also presents many challenges in data analysis and interpretation, due to the large amount of data collected. For example, conventional methods for land use and land cover classifications may not be applicable, due to "the curse of dimensionality." Therefore, these conventional methods may need a preprocessing step to transform high dimensional data to low dimensional data, by eliminating data redundancy. Due to its conceptual simplicity, principal component analysis (PCA) has been widely used for decades to reduce dimensionality. It is a useful technique if the spectral class structure of the transformed data is such that it is distributed along the first few axes. Otherwise, the transformed data may be similar to the original data. In such a case, the wavelet decomposition technique might be a better approach. Wavelet decomposition can reduce hyperspectral data in the spectral domain for each pixel. This will not only reduce the data volume, but will also preserve the distinction among spectral signatures that is useful for most pixel-based classifiers. This characteristic is related to the intrinsic property of wavelet transforms that preserve high- and low-frequency features during the signal decomposition, and therefore preserve peaks and valleys found in typical spectra. In general, most classification errors occur at the boundary between classes. Since wavelet decomposition is applied to each local pixel, a wavelet-based reduction might not well differentiate classes among neighborhood pixels in the spatial domain. PCA, however, can provide more local spatial information among neighborhood class pixels than wavelet.