  In this paper we study the compressive sensing effects on 2D signals
exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of
randomly under-sampled data is proposed. It is based on the analytically
determined threshold that precisely separates signal and non-signal components
in the 2D DFT domain. The algorithm operates fast in a single iteration
providing the accurate signal reconstruction. In the situations that are not
comprised by the analytic derivation and constrains, the algorithm is still
efficient and need just a couple of iterations. The proposed solution shows
promising results in ISAR imaging (simulated data are used), where the
reconstruction is achieved even in the case when less than 10% of data is
available.
