We propose a novel approach based on optimal transport (OT) for tackling the problem of highly mixed data in blind hyperspectral unmixing. Our method constrains the distribution of the estimated abundance matrix to resemble a targeted Dirichlet distribution more closely. The novelty lies in using OT to measure the discrepancy between the targeted and true abundance distributions, which we incorporate as a regularization term in our optimization problem. We demonstrate the efficiency of our method through a case study involving an unsupervised deep learning approach. Our experiments show that the proposed approach allows for a better estimation of the endmembers in the presence of highly mixed data, while displaying robustness to the choice of target abundance distribution.