Constrained Least Squares Algorithms for Nonlinear Unmixing of Hyperspectral Imagery

Hyperspectral unmixing is an important issue in hyperspectral image processing. In this paper, we transform the unmixing problem into a constrained nonlinear least squares (CNLS) problem by introducing the abundance sum-to-one constraint, abundance nonnegative constraint, and bound constraints on nonlinearity parameters. The new CNLS-based algorithms assume that the mixing mechanism of each observed pixel can be described by two forms. One is a sum of linear mixtures of endmember spectra and nonlinear variations in reflectance, and the other is a joint mixture resulting from the linearity and nonlinearity in hyperspectral data. For the former, an alternating iterative optimization algorithm is developed to solve the problem of CNLS. As for the latter, the structured total least squares optimization approach is used to obtain the abundance vectors and nonlinearity parameters simultaneously. Current mixing models can be interpreted by either or both of these two mechanisms. A comparative analysis based on Monte Carlo simulations and real data experiments is conducted to evaluate the proposed algorithms and five other state-of-the-art algorithms. Experimental results show that the proposed algorithms give outstanding performance of hyperspectral nonlinear unmixing for both synthetic data and real hyperspectral images, as satisfactory accuracy in term of abundance fractions and low computational complexity are observed.