Matrix data has arised in many field, especially in the field of image processing and computer vision. In traditional approaches, the original images need to be vectorized to one-dimension vectors, which may destroy the inherent structure of images. A novel geometrical sparse representation (GSR) model with single image is introduced in this paper that solves a model to measure the similarity between the input image and the single dictionary image. Unlike the traditional sparse representation model, the proposed model does not need to vectorize the image, so as to preserve the inherent geometrical structure of the image. We further introduce a binary coding method to preserve the local patterns of the image and enhance the sparsity of the GSR coefficients. Our method is used for face images with variations of structural noise (occlusion, illumination, etc.), extensive experiments show that our method can be competitive with or even superior to the baseline methods.

矩阵数据已经出现在许多领域，尤其是在图像处理和计算机视觉领域。在传统方法中，原始图像需要矢量化为一维矢量，这可能会破坏图像的固有结构。本文介绍了一种新颖的单图像几何稀疏表示（GSR）模型，该模型解决了一种用于测量输入图像与单字典图像之间相似度的模型。与传统的稀疏表示模型不同，所提出的模型不需要对图像进行矢量化处理，从而保留了图像的固有几何结构。我们进一步介绍一种二进制编码方法，以保留图像的局部图案并增强GSR系数的稀疏性。我们的方法用于结构噪声（遮挡，