  Deep neural networks based on unrolled iterative algorithms have achieved
remarkable success in sparse reconstruction applications, such as synthetic
aperture radar (SAR) tomographic inversion (TomoSAR). However, the currently
available deep learning-based TomoSAR algorithms are limited to
three-dimensional (3D) reconstruction. The extension of deep learning-based
algorithms to four-dimensional (4D) imaging, i.e., differential TomoSAR
(D-TomoSAR) applications, is impeded mainly due to the high-dimensional weight
matrices required by the network designed for D-TomoSAR inversion, which
typically contain millions of freely trainable parameters. Learning such huge
number of weights requires an enormous number of training samples, resulting in
a large memory burden and excessive time consumption. To tackle this issue, we
propose an efficient and accurate algorithm called HyperLISTA-ABT. The weights
in HyperLISTA-ABT are determined in an analytical way according to a minimum
coherence criterion, trimming the model down to an ultra-light one with only
three hyperparameters. Additionally, HyperLISTA-ABT improves the global
thresholding by utilizing an adaptive blockwise thresholding scheme, which
applies block-coordinate techniques and conducts thresholding in local blocks,
so that weak expressions and local features can be retained in the shrinkage
step layer by layer. Simulations were performed and demonstrated the
effectiveness of our approach, showing that HyperLISTA-ABT achieves superior
computational efficiency and with no significant performance degradation
compared to state-of-the-art methods. Real data experiments showed that a
high-quality 4D point cloud could be reconstructed over a large area by the
proposed HyperLISTA-ABT with affordable computational resources and in a fast
time.
