In hyperspectral imaging spectral unmixing is a data analysis process which involves the computation of the fractional contributions (abundances) of the spectral signatures of elementary materials (endmembers) to the measured spectra. The underlying image (forward) model can be formulated as a linear mixture of spectral signatures with nonnegative sparse coefficients. In addition, we also incorporate a data acquisition blurring matrix in the forward model. The reconstruction problem can then be formulated as a large scale, structured, constrained least squares problem. In this talk we show that by exploiting the structure of the coefficient matrix, and using known properties of the endmembers, iterative methods can be used to efficiently reconstruct the fractional abundance coefficients.