Robust hyperspectral signal unmixing in the presence of correlated noise

Hyperspectral imaging analysis aims at the estimation of the number of constituent substances, known as endmembers, their spectral signatures as well as their abundance fractions . Due to the nature of hyperspectral sensors, output data is mostly associated with correlated noise rather than with the white Gaussian noise considered in most of the analysis. In the presence of correlated noise, estimation of dimensionality with the assumption of white noise is associated with consider able error. This error in the very first step will be propagated to the next steps and fully invalidate the unmixing process. On the other hand, existing methods which consider a correlated noise are lacking in robustness to noise. A Whitened Noiseless Code-length method (WNCLM) is presented for hyperspectral signals dimension estimation and unmixing in the presence of spectrally or spatially correlated noise. Variance and correlation coefficients are calculated to estimate the noise correlation matrix. This matrix is further used to whiten the noise. New processed hyperspectral data then goes through a simultaneous denoising and Least Square Error (LSE) based unmixing process that leads to the estimation of data dimensionality. Some numerical simulations are provided to illustrate the effectiveness of our proposed method.