This paper proposes a joint reconstruction algorithm for compressed correlated images that are given under the form of linear measurements. We first propose a geometry based model in order to describe the correlation between visual information in pairs of images, which is mostly driven by the translational motion of objects or vision sensors. We consider the particular problem where one image is selected as the reference image and it is used as the side information for decoding the compressed correlated images. These compressed images are built on random measurements that are further quantized and entropy coded. The joint decoder first captures the most prominent visual features in the reference image using geometric basis functions. Since images are correlated, these features are likely to be present in the compressed images too, possibly with some small transformation. Hence, the reconstruction of the compressed image is based on a regularized optimization problem that estimates these features in the compressed images. The regularization term further enforces the consistency between the reconstructed images and the quantized measurements. Experimental results show that the proposed scheme is able to efficiently estimate the correlation between images. It further leads to good reconstruction performance. The proposed scheme is finally shown to outperform DSC schemes based on unsupervised disparity or motion learning as well as independent coding solutions based on JPEG-2000 from a rate-distortion perspective.