A method for reconstructing a digital image from a set of measurements includes providing a previous image frame in a time series of measurements of an image signal and a current image frame in the time series, calculating an estimated motion vector for a spatial point and current time point between the previous and current image frames, calculating a motion compensated current image frame from the previous image frame, estimating a known support set of a sparse signal estimate of the motion compensated current image frame where the support set comprises indices of non-zero elements of the sparse signal estimate, calculating a sparse signal corresponding to the current image frame whose support contains a smallest number of new additions to the known support set while satisfying a data consistency constraint, and correcting the motion compensated current image frame image frame from the sparse signal.