  Spectral unmixing (SU) is a technique to characterize mixed pixels in
hyperspectral images measured by remote sensors. Most of the spectral unmixing
algorithms are developed using the linear mixing models. To estimate endmembers
and fractional abundance matrices in a blind problem, nonnegative matrix
factorization (NMF) and its developments are widely used in the SU problem. One
of the constraints which was added to NMF is sparsity, that was regularized by
Lq norm. In this paper, a new algorithm based on distributed optimization is
suggested for spectral unmixing. In the proposed algorithm, a network including
single-node clusters is employed. Each pixel in the hyperspectral images is
considered as a node in this network. The sparsity constrained distributed
unmixing is optimized with diffusion least mean p-power (LMP) strategy, and
then the update equations for fractional abundance and signature matrices are
obtained. Afterwards the proposed algorithm is analyzed for different values of
LMP power and Lq norms. Simulation results based on defined performance metrics
illustrate the advantage of the proposed algorithm in spectral unmixing of
hyperspectral data compared with other methods.
