Hyperspectral unmixing based on sparsity is a research hotspot in recent years. This paper studies the hyperspectral unmixing algorithms based on L₁ regularization. First we analyzed three unmixing models, including unconstrained model, non-negative constraint model and full-constrained model. And then the corresponding algorithms are presented. In the end, both simulated and real hyperspectral data sets are used to compare and evaluate the proposed three hyperspectral unmixing algorithms. Experimental results demonstrate that three models all have good high-precision. The full constrained model achieves the best unmixing precision(SRE). The non-negative constrained model is better. And the unconstrained model is worst. In particular, the fully constrained model achieves the higher SRE under the low signal to noise ratio and a large amount of endmembers situation.