In super-resolution microscopy methods based on single-molecule switching, the rate of accumulating single-molecule activation events often limits the time resolution. Here we developed a sparse-signal recovery technique using compressed sensing to analyze images with highly overlapping fluorescent spots. This method allows an activated fluorophore density an order of magnitude higher than what conventional single-molecule fitting methods can handle. Using this method, we demonstrated imaging microtubule dynamics in living cells with a time resolution of 3 s.