Abstract In this article, a local structure adaptive total variation (LSATV) method for image restoration is presented. In our method, a discontinuity indicator is first proposed based on the eigenvalues of the structure tensor, which can effectively distinguish between edges and noises. Based on the proposed discontinuity indicator, a p norm is adaptively selected to match the local structure property of a pixel. Therefore, the proposed LSATV method inherits the advantages of both the Tikhonov regularization method and the total variation regularization method. Experimental results show the robustness of the proposed method and its superiority to state-of-the-art methods.