Basis Pursuit Denoising via Recurrent Neural Network Applied to Super-Resolving SAR Tomography

Abstract

Finding sparse solutions of underdetermined linear systems commonly requires the solving of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularized least squares minimization problem, which is also known as the basis pursuit denoising (BPDN). They are computationally expensive since they cannot be solved analytically. An emerging technique known as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deep unrolling</i> provided a good combination of the descriptive ability of neural networks, explainable, and computational efficiency for BPDN. Many unrolled neural networks for BPDN, e.g. learned iterative shrinkage thresholding algorithm and its variants, employ shrinkage functions to prune elements with small magnitude. Through experiments on synthetic aperture radar tomography (TomoSAR), we discover the shrinkage step leads to unavoidable information loss in the dynamics of networks and degrades the performance of the model. We propose a recurrent neural network (RNN) with novel sparse minimal gated units (SMGUs) to solve the information loss issue. The proposed RNN architecture with SMGUs benefits from incorporating historical information into optimization, and thus effectively preserves full information to the final output. Taking TomoSAR inversion as an example, extensive simulations demonstrated that the proposed RNN outperforms the state-of-the-art deep learning-based algorithm in terms of super-resolution power as well as generalization ability. It achieved 10% to 20% higher double scatterers detection rate and is less sensitive to phase and amplitude ratio difference between scatterers. Test on real TerraSAR-X spotlight images also shows high-quality 3-D reconstruction of test site.