Ultrafast ultrasound (US) imaging uses unfocused waves to insonify the whole medium of interest at once, allowing pulse-echo US imaging to achieve very high frame rates, at the cost of a lower image quality. In this paper, we present USSR, an UltraSound Sparse Regularization framework which permits high-quality imaging at fast rates and with a very low memory footprint. The framework, based on highly parallelizable, parametric, matrix-free formulations of the measurement model and its adjoint as well as on well-chosen sparsity priors, is implemented on multi-threaded architectures and evaluated on the publicly available PICMUS dataset.