Robust Endmember detection using L1 norm factorization

Given this model, spectral unmixing and endmember detection are the tasks of determining the endmembers and the proportions for every data point in the scene. Several endmember detection and spectral unmixing algorithms have been developed in the literature. However, the majority of these methods do not provide an autonomous way to estimate the number of endmembers and, thus, require the number of endmembers in advance. These methods include those based on Non-negative Matrix Factorization [3, 4], based on Indepenent Components Analysis [5, 6], and others [7, 8]. The number of endmembers is often unknown in advance. Methods to estimate the number of endmembers from a data set have been developed as well. These methods include Virtual Dimensionality (VD), Transformed Gerschogorin Disk (TGD), the Noise-Adjusted TGD, and the Partitioned NoiseAdjusted Principal Components Analysis (PNAPCA) methods [9–11]. The VD method estimates the number of endmembers using the eigenvalues of the covariance and correlation matrices of the hyperspectral data set. The number of endmembers is set to the number of eigenvalues from the covariance and correlation matrices that differ based on some computed threshold. Due to the variances used when computing the thresholds, the VD method can be sensitive to noise in the data. The PNAPCA method relies on the use of the Maximum Noise Fraction (MNF) algorithm [12]. MNF simultaneously diagonalizes the data covariance matrix and whitens the noise covariance matrix for a data set. This requires an estimate