Hyperspectral unmixing aims at determining the reference spectral signatures composing a hyperspectral image, their abundance fractions and their number. In practice, the spectral variability of the identified signatures induces significant abundance estimation errors. To address this issue, this paper introduces a new linear mixing model explicitly accounting for this phenomenon. In this setting, the extracted endmembers are interpreted as possibly corrupted versions of the true endmembers. The parameters of this model can be estimated using an optimization algorithm based on the alternating direction method of multipliers. The performance of the proposed unmixing method is evaluated on synthetic and real data.