Hyperspectral unmixing aims to identify the spectral characteristics of substances(endmembers) and spatial distribution(abundance) features of substances(end elements) from a blind source separation scenario.To address the challenges posed by a large number of mixed pixels in hyperspectral images,which can reduce unmixing accuracy,and the difficulty in accurately estimating the number of endmembers when hyperspectral data is contaminated with noise,a hyperspectral unmixing model that combines low rank relaxation and separable total variation prior information is proposed in this paper.Firstly,the local similarity of the logarithmic function is utilized to relax the nuclear norm based low rank expression,thereby suppressing minor components.Then,the anisotropic total variation is redefined as a separable expression to smooth the spectral characteristics and spatial abundance features.Finally,a set of efficient solvers is designed to obtain a closed form solution.The experimental results show that the proposed unmixing model can effectively improve the unmixing accuracy while suppressing the noise,which verifies the effectiveness of the model.