Sparse Approximation, Coherence and Use of Derivatives in Hyperspectral Unmixing

Recently, it has been shown that the spectral unmixing can be regarded as a sparse approximation problem. In our studies we employ predefined dictionaries containing the measured spectra of different materials in a hyperspectral image, where for each pixel the abundance vector can be estimated solving the $\ell_1$ optimization problem. This results in an automation of the unmixing procedure and enables using complex overcomplete dictionaries. However, the reflectance spectra of most materials are highly coherent and this could result in confusion in the mixture estimation. In this work we present a novel approach for spectral dictionary coherence reduction and discuss the feasibility of the methodologies in terms of mutual coherence and approximation error values using overcomplete dictionaries. We compare standard sparse unmixing procedures with our novel derivative method. The presented method was tested on both simulated hyperspectral image as well as on a AVIRIS data.