Tomographic Imaging of Sparse Low-Contrast Targets in Harsh Environments Through Matrix Completion

A new methodology that exploits the matrix completion (MC) paradigm is proposed to image weak and sparse scatterers in heavy noise conditions. The 2-D inverse problem, mathematically formulated under the first-order Born approximation, is addressed with a three-phase algorithm that consists of: 1) an initial estimation step where a preliminary reconstruction of the distribution of the contrast and the associated “confidence map” are computed by means of a Bayesian compressive sensing method; 2) a filtering step devoted to identify and discard the less reliable contrast coefficients; and 3) a final dielectric profile completion step aimed at recovering a faithful image of the whole scattering scenario by exploiting a customized MC procedure. Representative numerical results and comparisons with competitive state-of-the-art inversion techniques are reported and discussed to assess the accuracy, the robustness, and the numerical efficiency of the proposed approach.