Sparse approximations that are evaluated using overcomplete learned dictionaries are useful in many image processing applications such as compression, denoising and feature extraction. Incorporating shift invariance into sparse representation of images can improve sparsity while providing a good approximation. The K-SVD algorithm adapts the dictionary based on a set of training examples, without shift invariance constraints. This paper presents two algorithms for training dictionaries and evaluating shift-invariant sparse representations for image data. One is a modified version of the K-SVD algorithm and the other is a novel graph-based algorithm that adapts the dictionary and computes representations using a low complexity reconstruction procedure.