Compressive Sensing Imaging of Non-Sparse 2D Scatterers by a Total-Variation Approach Within the Born Approximation

The problem of imaging two-dimensional “non-sparse” scatterers with piecewise-constant contrast is solved through an innovative total-variation compressive sensing (TV-CS) technique. Under Born approximation (BA), the time-harmonic two-dimensional inverse scattering problem is reformulated into an equivalent Augmented Lagrangian one according to the TV-CS formulation. The resulting unconstrained functional is then minimized by means of a deterministic alternating direction algorithm. Selected results from a numerical assessment are discussed to give the interested reader some insights on the accuracy, the flexibility, the robustness, and the efficiency of the TV-CS inversion scheme also in comparison with available implementations of state-of-the-art inversion methods still formulated within the BA.