Unconstrained Linear Spectral Mixture Models for Spatial Information Extraction: A Comparative Study

Linear spectral unmixing remains an important subject of research in image processing community. It deals with disintegrating a pixel spectrum into its constituent spectra through a mixture model assuming that observed data are linear mixtures of two or more objects, representing a mixed pixel. The linear mixture model allows a number of target materials (classes) to be present, each contributing a fraction of its unique, fixed spectrum corresponding to the area occupied by that material in a pixel. The linear model is inverted to produce estimates of those fractional abundances. The optimal solution of the mixture model can be an unconstrained solution, partially constrained solution or a fully constrained solution when the abundance non-negativity and abundance sum-to-one constraints are imposed. Although constrained algorithms are appropriate for target quantification and for estimating abundance fractions, unconstrained models are more suitable for applications seeking target detection, identification and discrimination. In this paper we perform a comparative study of five unconstrained mixture models -- unconstrained least squares, orthogonal subspace projection, singular value decomposition, sparse unmixing via variable splitting and augmented Lagrangian (SUnSAL) and SUnSAL Total Variation (SUnSAL TV). The algorithms are tested on computer-simulated data of various signal to noise ratio and Landsat-5 TM data of an agricultural landscape and an urban scenario. The results were validated using descriptive statistics, correlation coefficient, RMSE, probability of success, and bivariate distribution function.