Enhanced Low-Rank Matrix Decomposition for High-Resolution UAV-SAR Imagery

Low-rank matrix decomposition is effective for sparse recovery. However, the conventions are limited in accuracy for high-resolution synthetic aperture radar (SAR) imagery due to the shrinkage effect in the cost function, which leads to biased estimates. To this end, an enhanced-low rank matrix decomposition (E-LRMD) SAR imaging algorithm is proposed, which employs a factor group-sparse regularization (FGSR) to approximate the intended cost function, so that the low-rank features can be represented. Since, the constructed regularization function is factorized, the singular value decomposition is avoided, and the computational burden can be reduced accordingly. Furthermore,
$\ell _{1}$
-norm is incorporated to encode the sparse feature. To incorporate with the enhancement of multiple features, the alternating direction method of multipliers (ADMM) framework is utilized. Therefore, both the low-rank and sparse features can be accurately recovered and enhanced, cooperatively, where the error propagation between the enhancement of multiple features is minimized. In the experiments, the effectiveness and robustness of the algorithm are verified by the simulated data and practical UAV-SAR data, respectively. Also, a phase transition diagram (PTD) experiment is carried out to analyse the advantages of the proposed algorithm in terms of quantitative aspects compared with the conventional methods.