Unsupervised Spectral Mixture Analysis with Hopfield Neural Network for hyperspectral images

Spectral Mixture Analysis (SMA) has been widely utilized to address the mixed-pixel problem in the quantitative analysis of hyperspectral remote sensing images. Recently Nonnegative Matrix Factorization (NMF) has been successfully utilized to simultaneously perform endmember extraction (EE) and abundance estimation (AE). In this paper, we formulate the solution of NMF by performing EE and AE iteratively. Based on our previous Hopfield Neural Network (HNN) based AE algorithm, an HNN is also constructed for EE to solve the multiplicative updating problem of NMF for SMA. As a result, SMA is conducted in an unsupervised manner and our algorithm is able to extract virtual endmembers without assuming the presence of spectrally pure constituents in hyperspectral scenes. We further extend such strategy to solve the constrained NMF (cNMF) models for SMA, where extra constraints are imposed to better model the mixed-pixel problem. Experimental results on both synthetic and real hyperspectral images demonstrate the effectiveness of our proposed HNN based unsupervised SMA algorithms.