Sparse unmixing is a crucial component in the analysis of hyperspectral images because of its ability to sparsely estimate abundances with a spectral library of considerable scale. The existing sparse unmixing techniques tend to employ the sparsity from a single perspective, i.e., ℓ1 or ℓ2,1. In this paper, we accurately estimate abundances from element-wise and channel-wise sparsity perspectives, which forms a new elastic reweighted sparse regularized sparse unmixing method, termed ElSpaSU. The proposed ElSpaSU method leverages the abundance matrix simultaneously using ℓ1 and ℓ2,1 sparsity regularizations. To further promote sparsity in the abundances, the proposed ElSpaSU incorporates two types of iterative reweighting weights. We utilize the alternating direction method of multipliers (ADMM) framework to ensure guaranteed convergence in solving the optimization problem. Experimental outcomes from simulated and real hyperspectral images highlight the remarkable efficacy of the suggested ElSpaSU in contrast to competing approaches.