Exact Multistatic Interferometric Imaging via Generalized Wirtinger Flow

• Published in: IEEE transactions on computational imaging Vol. 6; pp. 711 - 726
• Main Authors: Yonel, Bariscan, Son, Il-Young, Yazici, Birsen
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acoustics; Approximation methods; Born approximation; Correlation analysis; Geophysics; Image reconstruction; Imaging; interferometric inversion; Interferometry; Mathematical analysis; Matrix methods; Multi-static radar; Multistatic radar; non-convex optimization; Phase retrieval; Pixels; Radar; Radar imaging; Radar measurement; Receivers; Scattering; wirtinger flow
• ISSN: 2573-0436; 2333-9403
• DOI: 10.1109/TCI.2020.2967151

We present a novel, exact method to address the interferometric inversion problem for multistatic wave-based imaging based on Generalized Wirtinger Flow (GWF) [1]. Interferometric imaging is a relative of phase retrieval, which arises from crosscorrelating measurements from pairs of receivers. GWF provides a theoretical framework to process scattering data satisfying the Born approximation, and guarantees exact recovery of the underlying scene reflectivity vector from interferometric measurements if the discretized lifted forward model satisfies the restricted isometry property over rank-1, positive semi-definite matrices with a sufficiently small restricted isometry constant (RIC). To this end, we design a linear deterministic discrete lifted forward model for interferometric multistatic radar measurements such that the exact recovery conditions of GWF are satisfied. Our results identify a lower limit on the pixel spacing and the sample complexity for exact multistatic radar imaging. We provide a numerical study of our RIC and pixel spacing bounds on synthetic single scattering data, which show that GWF can achieve exact recovery with super-resolution. While our primary interest lies in radar imaging, our results are applicable to other multistatic wave-based imaging problems such as those arising in acoustics and geophysics.