Three-Dimensional SAR Imaging with Sparse Linear Array using Tensor Completion in Embedded Space

Abstract Due to the huge data storage and transmission pressure, sparse data collection strategy has provided opportunities and challenges for 3-D 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 3-D 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 3-D 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 3-D imaging algorithm using TC in embedded space is proposed to produce 3-D images with efficient side-lobes suppression. With the help of sparsity and low-rank property hidden in the 3-D 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 3-D imaging methods can be employed to obtain excellent imaging performance for the completed tensor. The proposed method achieves high resolution and low-level sidelobes 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 3-D 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.