Due to low light emission of fluorescent samples, live fluorescence microscopy imposes a tradeoff between spatiotemporal resolution and signal-to-noise ratio. This can result in images and videos containing motion blur or Poisson-type shot noise, depending on the settings used during acquisition. Here, we propose an algorithm to simultaneously denoise and temporally super-resolve movies of repeating microscopic processes that is compatible with any conventional microscopy setup that can achieve imaging at a rate of at least twice that of the fundamental frequency of the process (above 4 frames per second for a 2 Hz process). Our method combines low temporal resolution frames from multiple cycles of a repeating process to reconstruct a denoised, higher temporal resolution image sequence which is the solution to a linear program that maximizes the consistency of the reconstruction with the measurements, under a regularization constraint. This paper describes, in particular, a parallelizable superresolution reconstruction algorithm and demonstrates its application to live cardiac fluorescence microscopy. Using our method, we experimentally show temporal resolution improvement by a factor of 1.6, resulting in a visible reduction of motion blur in both on-sample and off-sample frames.