Morphologically Decoupled Multi-Scale Sparse Representation for Hyperspectral Image Analysis

Hyperspectral imagery has emerged as a popular sensing modality for a variety of applications, and sparsity based methods were shown to be very effective to deal with challenges coming from high dimensionality in most hyperspectral classification problems. In this work, we challenge the conventional approach to hyperspectral classification, that typically builds sparsity-based classifiers directly on spectral reflectance features or features derived directly from the data. We assert that hyperspectral image processing can benefit very significantly by decoupling data into geometrically distinct components since the resulting decoupled components are much more suitable for sparse representation based classifiers. Specifically, we apply morphological separation to decouple data into texture and cartoon-like components, which are sparsely represented using local discrete cosine bases and multiscale shearlets, respectively. In addition to providing sparser representation, this approach allows us to take advantage of the invariance properties of each basis within each geometrically distinct component of the data. Experimental results using real-world hyperspectral image datasets demonstrate the efficacy of the proposed framework for classifying multi-channel imagery under a variety of adverse conditions — in particular, small training sample size, additive noise, and rotational variabilities between training and test samples.