PECNet: a deep learning approach for rapid compensation of nonlinear phase errors in ground-based bistatic synthetic aperture radar lunar imaging

In ground-based bistatic synthetic aperture radar (Bi-SAR) lunar imaging, the traditional phase gradient autofocus (PGA) algorithm shows performance degradation in scenarios with insufficient strong scatterers. The minimum entropy algorithm (MEA) achieves high compensation accuracy but is slow. Existing deep learning methods rely on polynomial phase error priors or ideal supervised labels, demonstrating insufficient adaptability in Bi-SAR lunar imaging conditions where such labels are unavailable. Based on this, we improved the unsupervised AutoFocus network (AFnet) by removing its polynomial prior constraint, resulting in an AutoFocus network for phase error (AFnet-PE). This model is computationally fast but shows poor compensation accuracy in Bi-SAR lunar imaging scenarios, with some samples exhibiting compensation degradation. Therefore, we propose the phase error compensation network (PECNet), which enables fast, accurate compensation of nonlinear errors in Bi-SAR lunar imaging by integrating local feature extraction from a convolutional neural network with the global modeling capability of a transformer. The experimental results demonstrate that PECNet achieves a better balance between compensation effectiveness and runtime, resulting in overall performance compared with MEA, PGA, and AFnet-PE. The mean normalized entropy reduction rate relative to MEA of PECNet is 0.943. In terms of computational speed, PECNet significantly reduces runtime to 17.83 s compared with MEA, whereas PGA and AFnet-PE achieve even faster times of 8.97 and 1.67 s. However, PECNet produces no compensation degradation samples, whereas PGA and AFnet-PE have degradation sample proportions of 50.5% and 1.9%.