Manifold Low Rank and Sparse Tensor Method for High-Resolution Radar Imaging

High-resolution radar imaging with compressive sensing (CS) is significantly important and meaningful in practical applications, such as data collection burden reduction and resource allocation scheduling in a multifunctional radar. The class of matrix completion (MC) methods is a powerful tool to directly reconstruct the missing data to be applied in sparse radar imaging, which can overcome the discrete error drawback of traditional dictionary-based CS methods. In this article, we extend the MC method to tensor completion (TC) with multidimensional data representation, and a novel manifold low-rank and sparse TC (MLRSTC) radar imaging algorithm is proposed for enhanced sparse imaging performance. In the scheme, an attractive tensor radar data model is proposed, and the low-rank tensor property is discovered by capturing the latent and intrinsic data structure in high dimensions. In particular, the low-rankness superiority of the tensor model is confirmed by both the theoretical derivation and experimental analysis. Then, the Kronecker-basis-representation (KBR)-based tensor sparsity model is applied to format the proposed MLRSTC algorithm of sparse radar imaging, which can effectively promote the reconstruction of tensor data with enhanced low-rank property. Meaningfully, the proposed MLRSTC algorithm can work well under the condition of different sparse data sampling patterns. Next, the proposed MLRSTC algorithm is efficiently solved in an iterative manner under the framework of alternating direction method of multipliers (ADMMs) by updating the involved parameters in a closed-form solution. Finally, the experiments using both electromagnetic simulation and measured data are performed to confirm the effectiveness and superiority of the proposed MLRSTC algorithm beyond state-of-the-art (SOTA).