# Sparse regularization with a non-convex penalty for SAR imaging and autofocusing

arXiv: https://arxiv.org/abs/2108.09855 · HTML: https://mlsanity.com/paper/2108.09855/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2021.

## Built on by (most cited first, 1 of 1)

- [Diffusion Probabilistic Models for Compressive SAR Imaging](https://mlsanity.com/paper/2504.17053/) (2025)

## Abstract (arXiv)

In this paper, SAR image reconstruction with joint phase error estimation (autofocusing) is formulated as an inverse problem. An optimization model utilising a sparsity-enforcing Cauchy regularizer is proposed, and an alternating minimization framework is used to solve it, in which the desired image and the phase errors are optimized alternatively. For the image reconstruction sub-problem (f-sub-problem), two methods are presented capable of handling the problem's complex nature, and we thus present two variants of our SAR image autofocusing algorithm. Firstly, we design a complex version of the forward-backward splitting algorithm (CFBA) to solve the f-sub-problem iteratively. For the second variant, the Wirtinger alternating minimization autofocusing (WAMA) method is presented, in which techniques of Wirtinger calculus are utilized to minimize the complex-valued cost function in the f-sub-problem in a direct fashion. For both methods, the phase error estimation sub-problem is solved by simply expanding and observing its cost function. Moreover, the convergence of both algorithms is discussed in detail. By conducting experiments on both simulated scenes and real SAR images, the proposed method is demonstrated to give impressive autofocusing results compared to other state of the art methods.