Sparse representation of hyperspectral data using CUR matrix decomposition

We propose CUR methods for hyperspectral unmixing that decompose the data matrix into non-negative endmembers and abundance maps. The endmembers will be selected from a dictionary constructed from the data matrix. Each endmember will coincide with certain columns of the data matrix. By doing this we are assured that the dictionary will be physically meaningful and may be interpreted unambiguously from the data set. This assumption, that the endmembers are contained within the data, is called the pixel purity assumption. We compare two regularization terms to promote sparsity in our solutions, the first is ℓ₂ regularization and the second is vector ℓ₀ regularization. The methods are evaluated both on simulated data and a real hyperspectral image of an urban landscape.