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Multi-color fluorescent in-situ hybridization (M- FISH) selectively stains multiple DNA sequences using fluorescently labeled DNA probes. Proper interpretation of M-FISH images is often hampered by spectral overlap between the detected emissions of the fluorochromes. When using more than two or three fluorochromes, the appropriate combination of wide-band excitation and emission filters reduces cross-talk, but cannot completely eliminate it. A number of approaches -both hardware and software- have been proposed in the last decade to facilitate the interpretation of M-FISH images. The most used and efficient approaches use linear unmixing methods that algorithmically compute and correct for the fluorochrome contributions to each detection channel. In contrast to standard methods that require prior knowledge of the fluorochrome spectra, we present a new method, Non-Negative Matrix Factorization (NMF), that blindly estimates the spectral contributions and corrects for the overlap. Our experimental results show that its performance in terms of residual cross-talk and spot counting reliability outperforms the non-blind state-of-the-art method, the Non-Negative Least Squares (NNLS) algorithm.