Investigation on constrained matrix factorization for hyperspectral image analysis

Abstract — Matrix factorization is applied to unsupervised linear unmixing for hyperspectral imagery. The algorithm, called non-negative matrix factorization, is used. It imposes a constraint on the non-negativity of the amplitudes of the recovered endmember spectral signatures as well as their fractional abundances. This ensures the recovery of physically meaningful endmembers and their abundances. This algorithm is further modified to include the sum-to-one constraint such that the sum of the fractional abundances for each pixel is unity. Several practical implementation issues in hyperspectral image unmixng are discussed. Some preliminary results from AVIRIS experiments are presented. We also discuss the advantages and possible limitations of this method in hyperspectral image analysis. Keywords: matrix factorization; nonnegative matrix factorization; linear mixture model; unsupervised linear unmixing; hyperspectral imagery. I. I NTRODUCTION Linear unmixing analysis is a well-known technique in remote sensing image analysis. It is based on the fact that the rough spatial resolution permits different materials present in the area covered by a single pixel. The linear mixture model says that a pixel reflectance in a visible-near infrared multispectral or hyperspectral image is the linear mixture from all independent pure materials (endmembers) present in an image scene [1]. Let