Weighted Residual NMF With Spatial Regularization for Hyperspectral Unmixing

This letter proposes a weighted residual nonnegative matrix factorization (NMF) with spatial regularization to unmix hyperspectral (HS) data. NMF decomposes a matrix into the product of two nonnegative matrices. However, NMF is known to be generally sensitive to noise, which makes it difficult to retrieve the global minimum of the underlying objective function. To overcome this limitation, we include a residual weighting mechanism in the conventional NMF formulation. This strategy treats each row of the residual based on the weighting factor. In this manner, residuals with large values are penalized less, and residuals with small values are penalized more to make the NMF-based unmixing problem more robust. Furthermore, we include a weight term in the form of an
$\ell _{1}$
norm regularizer to provide spatial information on the abundance matrix. Experimental results are conducted to validate the effectiveness of the proposed method.