A smooth hyperspectral unmixing method using cyclic descent

Hyperspectral unmixing is the process where the reflectance spectrum from a mixed pixel is decomposed into separate distinct spectral signatures (endmembers). A mixed pixel results when spectra from more than one material is recorded by a sensor in one pixel. The goal of linear unmixing is to identify the number of endmembers in an image, the endmembers themselves and their abundances in each pixel. This paper presents a new smooth method for unmixing hyperspectral images using nonnegative cyclic descent. The proposed method uses iterative cyclic descent algorithm to find the endmembers and their abundances. The algorithm uses an ℓ₁ norm to promote sparseness in the abundances. Because the spectrum of the endmembers varies smoothly, a first order roughness penalty is added to discourage roughness in the endmembers. The algorithm does not use any prior information about the data. The method is tested using a real hyperspectral image of an urban landscape.