A graph Laplacian regularization for hyperspectral data unmixing
This is an incremental improvement for hyperspectral imaging analysis, addressing computational challenges in unmixing.
The paper tackled hyperspectral data unmixing by introducing a graph Laplacian regularization to promote smoothness and collaborative estimation in abundance maps, resulting in improved effectiveness compared to classical regularizations in simulations on synthetic data.
This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect spectrally and spatially similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the algorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral unmixing.