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 cross-correlating 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.

中文翻译：

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通过广义维廷格流进行精确的多静态干涉成像

我们提出了一种新颖、精确的方法来解决基于广义维廷格流 (GWF) [1] 的多静态波成像的干涉反演问题。干涉成像是相位反演的相对物，相位反演是由接收器对的互相关测量产生的。GWF 提供了一个理论框架来处理满足 Born 近似的散射数据，如果离散化提升前向模型满足 1 阶正半定矩阵的受限等距特性，则保证从干涉测量中准确恢复底层场景反射率向量足够小的受限等距常数 (RIC)。为此，我们为干涉多基地雷达测量设计了一个线性确定性离散提升前向模型，以满足 GWF 的精确恢复条件。我们的结果确定了精确多基地雷达成像的像素间距和样本复杂性的下限。我们提供了对合成单散射数据的 RIC 和像素间距边界的数值研究，这表明 GWF 可以实现超分辨率的精确恢复。虽然我们的主要兴趣在于雷达成像，但我们的结果也适用于其他基于多静波的成像问题，例如声学和地球物理学中出现的问题。我们提供了对合成单散射数据的 RIC 和像素间距边界的数值研究，这表明 GWF 可以实现超分辨率的精确恢复。虽然我们的主要兴趣在于雷达成像，但我们的结果也适用于其他基于多静波的成像问题，例如声学和地球物理学中出现的问题。我们提供了对合成单散射数据的 RIC 和像素间距边界的数值研究，这表明 GWF 可以实现超分辨率的精确恢复。虽然我们的主要兴趣在于雷达成像，但我们的结果也适用于其他基于多静波的成像问题，例如声学和地球物理学中出现的问题。