Sparsity-based autofocus for undersampled synthetic aperture radar

Abstract

Motivated by the field of compressed sensing and sparse recovery, nonlinear algorithms have been proposed for the reconstruction of synthetic aperture radar images when the phase history is under-sampled. These algorithms assume exact knowledge of the system acquisition model. In this paper we investigate the effects of acquisition model phase errors when the phase history is under-sampled. We show that the standard methods of autofocus, which are used as a post-processing step on the reconstructed image, are typically not suitable. Instead of applying autofocus as a post-processor, we propose an algorithm that corrects phase errors during the image reconstruction. The performance of the algorithm is investigated quantitatively and qualitatively through numerical simulations on two practical scenarios where the phase histories contains phase errors and are under-sampled.

Analysis of sparsity based joint SAR image reconstruction and autofocus techniques

“…Letting , can be expressed as: (7) In (7), both the image and the phase error vector should be solved jointly. Sparsity based SAR imaging and autofocus techniques [6], [8], [9] mainly try to solve similar optimization problems with minor variations. In [6], a Sparsity Driven Approach (SDA) is used and the cost function defined in (8) is minimized:…”

“…One of the most well known techniques is the phase gradient autofocus (PGA) [3], which corrects phases based on dominant targets. Although there are many other autofocus techniques for classical SAR imaging [4], [5] sparsity based SAR imaging and autofocus techniques have been proposed in the recent years [6]- [9].…”

“…Later authors extended this work in [8], where a sparsity based Expectation Maximization Matching Pursuit algorithm (EMMP) is proposed for joint SAR image reconstruction and phase error correction with lower computational complexity compared to convex optimization. In [9], another sparsity based autofocus (SBA) for joint SAR image reconstruction and phase error correction is given. It is stated that the performance of the method is superior to the post image processing phase correction methods.…”

“…It is stated that the performance of the method is superior to the post image processing phase correction methods. All of these sparse autofocus methods [6]- [9] are capable of SAR image reconstruction for the undersampled case. However no comparisons between these techniques are available in the literature in terms of required amount of measurements and sparsity relation, SNR, level of phase error corrected etc.…”

Autofocused compressive SAR imaging based on the alternating direction method of multipliers

“…There are several algorithms that can estimate and correct the phase error, however these algorithms have not been proven to work well in the context of compressed sensing. While sparsity-driven autofocused SAR imaging has been proposed before [1], [2], [3], [4], [5], computationally efficient algorithms for practical use remains a challenge. Our contribution here is an improved and computationally efficient alternating direction method of multipliers (ADMM) based algorithm for autofocused compressive SAR imaging.…”