Multilayer NMF for Blind Unmixing of Hyperspectral Imagery with Additional Constraints

Abstract

Due to the coincidence of hyperspectral reflectance nonnegativity (and its corresponding abundance) with nonnegative matrix factorization (<small>NMF</small>) methods, <small>NMF</small> has been widely applied to unmix hyperspectral images in recent years. However, many local minima persist because of the nonconvexity of the objective function. Thus, the nonnegativity constraint is not sufficient and additional auxiliary constraints should be applied to objective functions. In this paper, a new approach we call constrained multilayer <small>NMF</small> (<small>CMLNMF</small>), is proposed for hyperspectral data. In this approach, the mixed spectra are regarded as endmember signatures that has been contaminated by multiplicative noise. The purpose of <small>CMLNMF</small> is to eliminate noise by hierarchical processing until the endmember spectra are obtained. Also, the hierarchical processing is self-adaptive to make the algorithm more effective. Furthermore, in each layer two constraints are implemented on the objective function. One is sparseness on the abundance matrix and the other is minimum volume on the spectral matrix. The hierarchical processing separates the abundance matrix into a series of matrices that make the characteristic of sparseness more obvious and meaningful. The proposed algorithm is applied to synthetic data and real hyperspectral data for quantitative evaluation. According to the comparison with other algorithms, <small>CMLNMF</small> has better performance and provides effective solutions for blind unmixing of hyperspectral image data.