  Array synthetic aperture radar (SAR) three-dimensional (3D) imaging can
obtain 3D information of the target region, which is widely used in
environmental monitoring and scattering information measurement. In recent
years, with the development of compressed sensing (CS) theory, sparse signal
processing is used in array SAR 3D imaging. Compared with matched filter (MF),
sparse SAR imaging can effectively improve image quality. However, sparse
imaging based on handcrafted regularization functions suffers from target
information loss in few observed SAR data. Therefore, in this article, a
general 3D sparse imaging framework based on Regulation by Denoising (RED) and
proximal gradient descent type method for array SAR is presented. Firstly, we
construct explicit prior terms via state-of-the-art denoising operators instead
of regularization functions, which can improve the accuracy of sparse
reconstruction and preserve the structure information of the target. Then,
different proximal gradient descent type methods are presented, including a
generalized alternating projection (GAP) and an alternating direction method of
multiplier (ADMM), which is suitable for high-dimensional data processing.
Additionally, the proposed method has robust convergence, which can achieve
sparse reconstruction of 3D SAR in few observed SAR data. Extensive simulations
and real data experiments are conducted to analyze the performance of the
proposed method. The experimental results show that the proposed method has
superior sparse reconstruction performance.
