3-D SAR Imaging via Perceptual Learning Framework With Adaptive Sparse Prior

Mathematically, 3-D synthetic aperture radar (SAR) imaging is a typical inverse problem, which, by nature, can be solved by applying the theory of sparse signal recovery. However, many reconstruction algorithms are constructed by exploring the inherent sparsity of imaging space, which may cause unsatisfactory estimations in weakly sparse cases. To address this issue, we propose a new perceptual learning framework, dubbed as PeFIST-Net, for 3-D SAR imaging, by unfolding the fast iterative shrinkage-thresholding algorithm (FISTA) and exploring the sparse prior offered by the convolutional neural network (CNN). We first introduce a pair of approximated sensing operators in lieu of the conventional sensing matrices, by which the computational efficiency is highly improved. Then, to improve the reconstruction accuracy in inherently nonsparse cases, a mirror-symmetric CNN structure is designed to explore an optimal sparse representation of roughly estimated SAR images. The network weights control the hyperparameters of FISTA by elaborated regularization functions, ensuring a well-behaved updating tendency. Unlike directly using pixelwise loss function in existing unfolded networks, we introduce the perceptual loss by defining loss term based on high-level features extracted from the pretrained VGG-16 model, which brings higher reconstruction quality in terms of visual perception. Finally, the methodology is validated on simulations and measured SAR experiments. The experimental results indicate that the proposed method can obtain well-focused SAR images from highly incomplete echoes while maintaining fast computational speed.