Blind linear unmixing (BLU) methods allow the separation of multi and hyperspectral data into end-members and abundance maps in an unsupervised fashion. However, due to incident noise, the abundance maps can exhibit high presence of granularity. To address this problem, in this paper, we present a novel proposal for BLU that considers spatial coherence in the abundance estimations, through a total spatial variation component. The proposed BLU formulation is based on the blind end-member and abundance extraction perspective with total spatial variation (EBEAE-STV). In EBEAE-STV, internal abundances are added to incorporate the spatial coherence in the cost function, which is solved by a coordinates descent algorithm. The results with synthetic data show that the proposed algorithm can significantly decrease the granularity in the estimated abundances, and the estimation errors and computational times are lower compared to state of the art methodologies.Clinical relevance- The proper and robust estimation of end-members and their respective contributions (abundances) in multi-spectral and hyper-spectral images from the proposed EBEAE-STV methodology might provide useful information in several biomedical applications, such as chemometric analysis on different biological samples, tumor identification and brain tissue classification for hyper-spectral imaging, among others.