# Sub-Nyquist SAR Imaging and Error Correction Via an Optimization-Based Algorithm

## TL;DR

This paper introduces a new optimization algorithm to improve sub-Nyquist SAR imaging and correct errors, enhancing image quality and performance.

## Contribution

A reweighted optimization algorithm, pseudo-ℒ0-norm, is proposed to address parameter tuning and low SNR issues in sub-Nyquist SAR.

## Key findings

- The proposed algorithm improves SAR image recovery with better resistance to low SNR.
- Experiments show the algorithm outperforms existing methods in simulated and real-world scenarios.
- The error correction method effectively reduces motion-induced defocusing.

## Abstract

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time–space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal–noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ0-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy–Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ0-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm.