Compressed sensing theory reduces lengthy acquisition time in MRI at the expense of computationally demanding iterative reconstruction. Usually, reconstruction is performed offline once all the data have been collected. Here, we introduce an online CS reconstruction framework that interleaves acquisition and reconstruction steps in a convex setting and permits the delivery of intermediate images on the scanner console during acquisition. In particular, the sum of acquisition and reconstruction times is reduced without compromising image quality. The gain of this strategy is shown both on retrospective Cartesian and prospective non-Cartesian under-sampled ex-vivo baboon brain data at 7T with an in-plane resolution of 400μm.