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This paper deals with nonnegative matrix factorization (NMF) dedicated to unmixing of hyperspectral images (HSI). We propose several improvements to better relate the output endmember spectra to the physical properties of the input data: firstly, we introduce a regularization term which enforces the closeness of the output endmembers to automatically selected reference spectra. Secondly, we account for these reference spectra and their locations in the initialization matrices. We exemplify our methods on self-acquired HSIs. The first scene is compound of leaves at the macroscopic level. In a controlled environment, we extract the spectra of three pigments. The second scene is acquired from an airplane: we distinguish between vegetation, water, and soil.

In the literature, there are several methods for multilinear source separation. We find the most popular ones such as nonnegative matrix factorization (NMF), canonical polyadic decomposition (PARAFAC). In this paper, we solved the problem of the hyperspectral imaging with NMF algorithm. We based on the physical property to improve and to relate the output endmembers spectra to the physical properties of the input data. To achieve this,we added a regularization which enforces the closeness of the output endmembers to automatically selected reference spectra. Afterwards we accounted for these reference spectra and their locations in the initialization matrices. To illustrate our methods, we used self-acquired hyperspectral images (HSIs). The first scene is compound of leaves at the macroscopic level. In a controlled environment, we extract the spectra of three pigments. The second scene is acquired from an airplane: We distinguish between vegetation, water, and soil.

There are two main contributions in this paper. Firstly, we estimate the rank for the truncation of the Parafac decomposition in an optimal sense. For this, we propose a least squares criterion and justify the choice of the fast Nelder-Mead method to minimize this criterion. Secondly, we combine the truncation of the Parafac decomposition with multidimensional wavelet packet transform. A single rank value is estimated for each decomposition level, which simplifies the implementation. We exemplify the proposed method with an application to multispectral image denoising: we study the performance of the proposed method based on Parafac decomposition, compared to ForWaRD