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.

Tomographic Imaging of Sparse Low-Contrast Targets in Harsh Environments Through Matrix Completion / Oliveri, Giacomo; Salucci, Marco; Anselmi, Nicola. - In: IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. - ISSN 0018-9480. - 2018, 66:6(2018), pp. 2714-2730. [10.1109/TMTT.2018.2825393]

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

Oliveri, Giacomo;Salucci, Marco;Anselmi, Nicola
2018

Abstract

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.
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Oliveri, Giacomo; Salucci, Marco; Anselmi, Nicola
Tomographic Imaging of Sparse Low-Contrast Targets in Harsh Environments Through Matrix Completion / Oliveri, Giacomo; Salucci, Marco; Anselmi, Nicola. - In: IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. - ISSN 0018-9480. - 2018, 66:6(2018), pp. 2714-2730. [10.1109/TMTT.2018.2825393]
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