We present a formulation of the linear sampling method (LSM) for reconstructing target shape from spatially sparse data sets. The technique compensates for a lack of spatial data by incorporating $a$ priori propagation information into the LSM inversion. A constraint is placed on the LSM solution that enforces a phase relationship across frequency that is determined by the electrical path length between the array transmitters and the imaging scene pixels. The effect of the constraint is that image artifacts that do not evince the expected phase relationship according to their position relative to the array are suppressed. We apply the proposed technique to simulated and experimental sparse-aperture data sets and show that the resulting imagery is significantly more faithful to the true target shape as compared to the imagery created with the standard LSM.

中文翻译：

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使用相位延迟频率变化约束的稀疏孔径数据集合的定性逆散射

我们提出了一种用于从空间稀疏数据集重建目标形状的线性采样方法 (LSM) 的公式。该技术通过将 $a$ 先验传播信息合并到 LSM 反演中来弥补空间数据的缺乏。对 LSM 解决方案施加了一个约束，该解决方案强制执行跨频率的相位关系，该关系由阵列发射器和成像场景像素之间的电路径长度确定。该约束的效果是抑制了根据其相对于阵列的位置不表现出预期相位关系的图像伪影。