Sparse representations for classification of high dimensional multi-sensor geospatial data

Modern active and passive geospatial sensing modalities often result in high dimensional feature spaces. Hyper-spectral imagery results in per-pixel spectral “signatures” that represent the reflectance/radiance over hundreds of contiguous spectral bands. Likewise, full-waveform LiDAR systems record the entire waveform of the return Laser pulse. Although the resulting feature spaces are high dimensional, the underlying dimensionality of the information content is often small (i.e., information resides in a lower dimensional subspace), and such data is often sparsely represented in an appropriate dictionary. In recent work, sparse representation based classification has been utilized for effective face recognition tasks. The traditional solution is posed as an optimization problem to learn the representation of test samples using the entire training dictionary under the constraint of sparsity - i.e., Sparse Representation based Classification (SRC). Although this has resulted in promising performance for face recognition tasks (where the number of classes is very large), and to some extent for geospatial image analysis tasks, we contend that the SRC formulation should be modified to yield robust performance for traditional image analysis tasks where the number of classes is not large. In recent work, we developed an alternate approach to use sparse representations for classification of hyperspectral imagery. In this paper, we develop a subspace learning preprocessing that effectively reduces the dimensionality of high dimensional geospatial data (both hyperspectral imagery, and full-waveform LiDAR data), and demonstrate its efficacy when combined with this recently developed sparse representation approach.