Semi-NMF Regularization-Based Autoencoder Training for Hyperspectral Unmixing

Hyperspectral Unmixing (HSU) refers to the procedure of decomposing measured pixel spectra into a set of constituent spectral signatures known as endmembers and a corresponding set of fractional mixing ratios. In this work, we propose a novel autoencoder training procedure with adaptive proximal regularization, designed for performing the semi-nonnegative matrix factorization (semi-NMF) that manifests in the hyperspectral unmixing application. The proposed regularization of the autoencoder parameters is based on the Karush-Kuhn-Tucker (KKT) optimality conditions associated with the semi-NMF optimization that underlies the HSU problem. We invoke convex analysis to develop a proximal regularization scheme that encourages the trained autoencoder to encapsulate the properties of the linear mixture generative model of the hyperspectral images. We evaluate the performance of the proposed regularized autoencoder and demonstrate its superior performance against a conventionally-trained autoencoder in performing semi-NMF factorization of synthetic data matrices and unmixing of semi-synthetic hyperspectral images.