In this paper, we present a compressed sensing model for 2D Full Matrix Capture data from a uniform linear array. Data is reconstructed via a matrix-free implementation of the Total Focusing Method (TFM) combined with the Fast Iterative Shrinkage/ Thresholding Algorithm. This results in reduced measurement times and data volumes with-out sacrificing image quality. Our approach is com-pared to standard TFM by applying the techniques on real measurement data, both synthetically compressed and complete.