An atomic autoencoder is a neural network architecture that decomposes an image as a sum of low dimensional atoms. While it is efficient for image datasets which are well represented by this summation model, it is more limited for the representation of more generic images. In this article, we propose a new atomic model, the max-sparsity model to better represent images. We study some theoretical properties of this model and implement the corresponding atomic autoencoder. We show experimentally that it leads to a sparse decomposition of input images with interpretable low-level visual features. With this new architecture, we solve a super resolution inverse problem via a projected gradient descent that uses the trained network as a projection operator. The resulting estimation shows improved robustness compared to previous architectures.