I will illustrate in this talk how computational neuroscience may inspire and be inspired by mathematical image processing. Focusing on efficiently representing natural images in the primary visual cortex, we derive an event-based adaptive algorithm inspired by statistical inference, Matching Pursuit and Hebbian learning. This algorithm allows to learn efficient "edge-like" receptive fields similarly to Independent Components Analysis. The correlation-based inhibition has been shown to be a necessary condition for the fomation of this type of receptive fields and shows the putative functional role of lateral propagation of information in cortical layers. I’ll first present state-of-the-art neural algorithms for this task, the results of a detailed analysis of this Sparse Hebbian Learning algorithm and finally draw a comparison with similar strategies.