An improved NMF algorithm based on spatial and abundance constraints

Hyperspectral imagery has been applied widely in military and civilian fields. However, mixed pixels can be commonly found in this type of image due to limitation of spatial resolution. This not only influences the precision of object recognition and classification, but also becomes an obstacle for quantification analysis of the imagery content. Spectral unmixing technique is a process aiming at identifying the constituent materials and estimating the corresponding fractions from hyperspectral imagery of a scene. Furthermore, Non-negative matrix factorization (NMF) is one effective linear spectral mixture model, finding endmembers and estimating the abundances simultaneously. But, applying the original NMF algorithm directly to decomposition of mixed pixels will result in local minimum and slow convergence. In this paper, spatial structure feature around endmembers and statistical characteristic of abundances are fully considered, and a new constrained objective function for non-negative matrix factorization algorithm is proposed based on the traditional smoothness constrained NMF. Firstly, spectral angle mapper (SAM) is joined into the smoothness constraint, which may reduce influence of noise and anomaly around the endmember by combining pixel spatial similarity and spectral similarity together. Secondly, a constraint for abundance covariance is added into the function in order to find endmembers making estimated abundance more stable, following the principle of maximum likelihood estimating. The original NMF algorithm, smoothness constrained NMF algorithm and the prompted algorithm are tested on simulation image. As expected, the experimental results show the effectiveness of the proposed approach.