Spectral image processing using sparse linear transforms

We propose the employment of nonnegative sparse linear feature extraction as a tool for unsupervised spectral unmixing. Sparse feature extraction can be seen as a general linear unmixing approach that maps the data into a new dimensional space in which each of the components has only a limited number of non-zero values. Unlike other transforms that target decorrelation or statistical independence, our focus is on the enforcement of sparseness by imposing restrictions (such as cardinality or norm relationships), as well as nonnegativity. When compared to the linear mixing model, the sparse components can be naturally associated to the abundance of endmembers, and the inverse transform to the endmembers. Our approach is a variant of a well known technique based on Nonnegative Matrix Factorization (NMF). In most of the cases, the NMF components are produced using a gradient descent optimization algorithm that was previously shown to converge. To validate our approach we use quantitative (classification) and qualitative (visualization) analysis of hyperspectral data sets.