Automatic Target Recognition (ATR) algorithms classify a given Synthetic Aperture Radar (SAR) image into one of the known target classes using a set of training images available for each class. Recently, learning methods have shown to achieve state-of-the-art classification accuracy if abundant training data is available, sampled uniformly over the classes, and their poses. In this paper, we consider the task of ATR with a limited set of training images. We propose a data augmentation approach to incorporate domain knowledge and improve the generalization power of a data-intensive learning algorithm, such as a Convolutional neural network (CNN). The proposed data augmentation method employs a limited persistence sparse modeling approach, capitalizing on commonly observed characteristics of wide-angle synthetic aperture radar (SAR) imagery. Specifically, we exploit the sparsity of the scattering centers in the spatial domain and the smoothly-varying structure of the scattering coefficients in the azimuthal domain to solve the ill-posed problem of overparametrized model fitting. Using this estimated model, we synthesize new images at poses and sub-pixel translations not available in the given data to augment CNN's training data. The experimental results show that for the training data starved region, the proposed method provides a significant gain in the resulting ATR algorithm's generalization performance.