Generally, the content of the hyperspectral image pixel is a mixture of the reflectance spectra of the different components in the imaged scene. In this paper, we consider a linear mixing model where the pixels are linear combinations of those reflectance spectra, called endmembers, and linear coefficients corresponding to their abundances. An important issue in hyperspectral imagery consists in unmixing those pixels to retrieve the endmembers and their corresponding abundances. We consider the unmixing issue in the presence of small targets, that is, their endmembers are only contained in few pixels of the image. We introduce a thresholding method relying on Non-negative Matrix Factorization to detect pixels containing rare endmembers. We propose two resampling methods based on bootstrap for spectral unmixing of hyperspectral images to retrieve both the dominant and rare endmembers. Our experimental results on both simulated and real world data demonstrate the efficiency of the proposed method to estimate correctly all the endmembers present in hyperspectral images, in particular the rare endmembers.