Due to the huge data storage and transmission pressure, sparse data collection strategy has provided opportunities and challenges for 3D SAR imaging. However, sparse data brought by the sparse linear array will produce high-level side-lobes, as well as the aliasing and the false-alarm targets. Simultaneously, the vectorizing or matrixing of 3D data makes high computational complexity and huge memory usage, which is not practicable in real applications. To deal with these problems, tensor completion (TC), as a convex optimization problem, is used to solve the 3D sparse imaging problem efficiently. Unfortunately, the traditional TC methods are invalid to the incomplete tensor data with missing slices brought by sparse linear arrays. In this paper, a novel 3D imaging algorithm using TC in embedded space is proposed to produce 3D images with efficient side-lobes suppression. With the help of sparsity and low-rank property hidden in the 3D radar signal, the incomplete tensor data is taken as the input and converted into a higher order incomplete Hankel tensor by multiway delay embedding transform (MDT). Then, the tucker decomposition with incremental rank has been applied for completion. Subsequently, any traditional 3D imaging methods can be employed to obtain excellent imaging performance for the completed tensor. The proposed method achieves high resolution and low-level side-lobes compared with the traditional TC-based methods. It is verified by several numerical simulations and multiple comparative studies on real data. Results clearly demonstrate that the proposed method can generate 3D images with small reconstruction error even when the sparse sampling rate or signal to noise ratio is low, which confirms the validity and advantage of the proposed method.

由于巨大的数据存储和传输压力，稀疏数据采集策略为3D SAR成像提供了机遇和挑战。然而，稀疏线性阵列带来的稀疏数据会产生高级旁瓣，以及混叠和误报目标。同时，3D 数据的矢量化或矩阵化使得计算复杂度高，内存占用大，这在实际应用中是不切实际的。为了解决这些问题，张量补全（Tensor completion，TC）作为一个凸优化问题，被用来有效地解决 3D 稀疏成像问题。遗憾的是，传统的 TC 方法对稀疏线性阵列带来的切片缺失的不完整张量数据无效。在本文中，提出了一种在嵌入式空间中使用 TC 的新型 3D 成像算法，以生成具有有效旁瓣抑制的 3D 图像。借助隐藏在 3D 雷达信号中的稀疏性和低秩特性，将不完全张量数据作为输入，通过多路延迟嵌入变换 (MDT) 将其转换为更高阶的不完全汉克尔张量。然后，已应用具有递增秩的 tucker 分解来完成。随后，可以采用任何传统的 3D 成像方法来获得完整张量的出色成像性能。与传统的基于 TC 的方法相比，所提出的方法实现了高分辨率和低电平旁瓣。通过多次数值模拟和对真实数据的多次比较研究验证了这一点。