Similarity-Guided and ℓ_p-Regularized Sparse Unmixing of Hyperspectral Data

In this letter, we propose a novel sparse unmixing model combined with two effective regularization terms: one is a similarity-weighting constraint, and the other is the ℓ_p (0 < p < 1) norm sparse regularization. The former utilizes the spatial structural correlation, which is presented in the hyperspectral data, to guide the abundance estimation. When compared with the existing graph Laplacian regularization, our similarity-weighting constraint avoids large matrix inversion, and thus, it can be efficiently solved. As for the ℓ_p-norm, it has numerical advantages over the convex ℓ₁-norm and better approximates the ℓ_o-norm theoretically. Moreover, the ℓ_p-norm regularizer can simultaneously promote sparsity and enforce the abundance sum-to-one constraint. Therefore, this term yields more desirable results in practice. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed model.