1. A computer implemented method of reconstructing a digital image from a set of measurements, the method performed by the computer comprising the steps of: providing a previous image frame corresponding to a previous time point in a time series of measurements of an image signal, and a current image frame corresponding to a current time point in said time series; calculating an estimated motion vector d t−1 for spatial point (n 1 , n 2 ) and current time point t between the previous image frame corresponding to the previous time point and the current image frame corresponding to the current time point; updating a motion compensated current image frame f t (n 1 , n 2 ) from the previous image frame f t−1 (n 1 , n 2 ) as f t (n 1 , n 2 )=f t−1 (n l +d 1 (n 1 , n 2 , t), n 2 +d 2 (n 1 , n 2 , t)); calculating a sparse signal estimate of the motion compensated current image frame x t based on the motion compensated image frame f t and a sparsity transform (ψ); estimating a known support set of the sparse signal estimate of the motion compensated current image frame x t , wherein the support set of the sparse signal estimate 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.