This letter proposes a simple, fast yet efficient sparse hyperspectral unmixing algorithm. The proposed method consists of three main steps. First, a coarse approximation of the hyperspectral image is built using a off-the-shelf segmentation algorithm. Then, a low-resolution approximation of the abundance map is estimated by solving a weighted ℓ1-regularized problem on this coarse approximation of the hyperspectral data. Finally, this low-resolution abundance map is subsequently used to design a sparsity-promoting penalization which acts as a spatial regularization informed by the coarse abundance map. It is incorporated into another weighted ℓ1-regularized problem whose solution is a higher resolution abundance map. The computational efficiency of the two last steps is ensured by solving the two underlying optimization problems using an alternating direction method of multipliers. Extensive experiments conducted on simulated and real data show the effectiveness of the proposed method.