Space-frequency sparse regularization for the linear sampling method

The Linear Sampling Method (LSM) is a promising inverse scattering approach that offers several desirable qualities over traditional filtered back-projection and non-linear optimization approaches. The quality of the reconstructions depends heavily on the availability of dense multi-static far-field data. Unfortunately data sets for radar imaging rarely satisfy this requirement, and hence require the extension of the LSM to sparse limited aperture data. The present work attempts this extension by leveraging the observed smoothness behavior of the far-field solution density with respect to frequency. In particular we see that the far-field density has small variation in frequency. This observation, combined with previous results, suggests solving the far-field equation with the constraint that the variation in both space and frequency should be minimal.