A critical goal of vision is to detect changes in light intensity, even when these changes are blurred by the spatial resolution of the eye and the motion of the animal. Here we describe a recurrent neural circuit in Drosophila that compensates for blur and thereby selectively enhances the perceived contrast of moving edges. Using in vivo, two-photon voltage imaging, we measured the temporal response properties of L1 and L2, two cell types that receive direct synaptic input from photoreceptors. These neurons have biphasic responses to brief flashes of light, a hallmark of cells that encode changes in stimulus intensity. However, the second phase was often much larger than the first, creating an unusual temporal filter. Genetic dissection revealed that recurrent neural circuitry strongly shapes the second phase of the response, informing the structure of a dynamical model. By applying this model to moving natural images, we demonstrate that rather than veridically representing stimulus changes, this temporal processing strategy systematically enhances them, amplifying and sharpening responses. Comparing the measured responses of L2 to model predictions across both artificial and natural stimuli revealed that L2 tunes its properties as the model predicts in order to deblur images. Since this strategy is tunable to behavioral context, generalizable to any time-varying sensory input, and implementable with a common circuit motif, we propose that it could be broadly used to selectively enhance sharp and salient changes.