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In this paper, a novel adaptive algorithm for spectral unmixing in hyperspectral images (HSIs) is proposed. Many of the existing spectral unmixing algorithms, under the assumption of the linear model for the spectral mixing phenomenon, attempt to estimate the signatures of available materials in the observed HSI image. Then, based on the similarity between the estimated spectral signatures and the available spectral signatures in the spectral library, they identify the materials in the HSI and estimate their relative abundances. While the spectral library, as prior knowledge, has not been directly considered in the founding of existing algorithms, the proposed method is directly concentrated on the spectral signatures library. Assuming the linear spectral mixing model, the proposed method takes a set of spectral signatures which are probably present in the observed HSI. Then, based on a non-statistical approach, the normalized least mean square (NLMS) adaptive algorithm is engaged to estimate a weight vector for each spectral signature in the selected set in such a way that each weight vector and its corresponding spectral signature are non-orthogonal whereas the weight vector of each spectral signature is almost orthogonal to the other spectral signatures. A synthetic dataset of hyperspectral images is considered to evaluate the performance of the proposed method. The evaluation results show that the proposed method outperforms its counterparts in low signal to noise ratio (SNR). [ABSTRACT FROM AUTHOR]