A Blind Spectral Unmixing in Wavelet Domain

Abstract

In this article, a wavelet-based energy minimization framework is developed for joint estimation of endmembers and abundances without assuming pure pixels while considering noisy scenario. Spectrally dense and overlapped hyperspectral data are represented using biorthogonal wavelet bases that yield a compact linear mixing model in the wavelet domain. It acts as the data term and helps to reduce solution space of the unmixed components. Three prior terms are incorporated to better handle the ill-posedness, i.e., the logarithm of determinant volume regularizer enforces minimum endmember simplex, smoothness (spatial) prior to individual abundance maps, and spectral constraint through learning dictionary of abundances. Alternating nonnegative least-squares is employed to optimize the regularized and constrained nonnegative matrix factorization functional in the wavelet domain. We conduct theoretical analysis, discuss convergence and algorithmic details. Experiments are conducted on synthetic and three real benchmark hyperspectral data AVIRIS Cuprite, HYDICE Urban, and AVIRIS Jasper Ridge. The efficacy of the proposed algorithm is evaluated by comparing results with state of the art.

Keywords

• Blind spectral unmixing
• compact linear mixing model (LMM)
• energy minimization
• hyperspectral imaging
• regularized nonnegative matrix factorization (NMF)
• sparse representation