This paper introduces an online optimization algorithm for dictionary learning, which is designed to adapt a dictionary to specific data, particularly useful in signal reconstruction and classification tasks. The algorithm is based on stochastic approximations and is scalable to large datasets with millions of training samples. It converges to a stationary point of the objective function with probability one, as demonstrated by a convergence proof. Experimental results on natural images show that the algorithm outperforms classical batch algorithms in terms of both speed and dictionary quality, both for small and large datasets. The paper also discusses improvements to the algorithm, such as handling fixed-size datasets and mini-batch extensions, and applies the learned dictionary to a challenging image inpainting task on a 12-Megapixel photograph.This paper introduces an online optimization algorithm for dictionary learning, which is designed to adapt a dictionary to specific data, particularly useful in signal reconstruction and classification tasks. The algorithm is based on stochastic approximations and is scalable to large datasets with millions of training samples. It converges to a stationary point of the objective function with probability one, as demonstrated by a convergence proof. Experimental results on natural images show that the algorithm outperforms classical batch algorithms in terms of both speed and dictionary quality, both for small and large datasets. The paper also discusses improvements to the algorithm, such as handling fixed-size datasets and mini-batch extensions, and applies the learned dictionary to a challenging image inpainting task on a 12-Megapixel photograph.