Sparse ISAR Imaging via Frequency-Selective Atomic Norm Minimization and Accelerated ADMM

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Abstract
Inverse synthetic aperture radar (ISAR) imaging technique has shown significant potential in civilian and military fields. However, radar systems encounter serious obstacles in acquiring long or full apertures. ISAR imaging targets exhibit sparsity in the spatial domain, which is beneficial for sparse recovery (SR) methods to achieve aperture reconstruction. This paper proposes the fast frequency-selective (FS) gridless sparse ISAR imaging methods to achieve high-precision aperture reconstruction, which fully considers the advantages of gridless techniques, structured model and prior knowledge. Usually, the FS atomic norm minimization (ANM) (FSANM) encodes the prior knowledge as a additional constraint into semi-positive definite programming (SDP), resulting in high computational complexity. The proposed method assumes that the selected frequency range follows the prior probability distribution, which is used to construct a weighting function for the atoms. Meanwhile, vandermonde decomposition and linear interpolation are employed to enhance the selection probability of adjacent atom. Then, a non-conveax metric has been implemented to enhance atomic sparsity. Although the alternating direction method of multipliers (ADMM) typically provides a more efficient solution for semidefinite programming problems, the standard eigen decomposition still faces problem of high computational complexity. Finally, the Lanczos decomposition algorithm is employed to achieve faster eigen-decomposition, thereby enhancing the computational efficiency of ISAR imaging. The experimental results of the simulated and measured data show that compared with the FSANM method, the proposed method has higher computational efficiency and better imaging performance under lower signal-to-noise ratio and data rate.

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