Sparsity-based methods for interrupted radar data reconstruction

Missing radar data may be reconstructed by using the structure present in surrounding data to make intelligent estimates of values at missing locations. We formulate the interrupted radar data scenario as an ℓ ₁- regularized least squares problem, and take advantage of the radar data's demonstrated sparsity in the discrete Fourier domain. Applying the split-variable augmented Lagrangian technique results in an iterative algorithm consisting of two alternating minimizations. The fast algorithm avoids explicit linear inverse solutions, and demonstrates good phase history reconstruction and improved imaging irrespective of the structure of the data loss. Experimental results are presented for synthetic aperture radar (SAR) image formation; however, the approach may also be used with other types of radar data.