Unsupervised SAR Despeckling via Modified Deep Image Prior with Dynamic Convergence Control

Abstract

Speckle, a signal dependent noise, affects different imaging techniques such as Synthetic Aperture Radar (SAR), photon-limited optical imaging and medical ultrasound. While the Deep Image Prior framework can despeckle SAR images with changes to parameters like learning rate or by converting it into log-domain, it is statistically inconsistent with speckle due to its Mean Square Error (MSE) loss function. In this work, we propose a modified Deep Image Prior framework that has been adapted for speckle suppression by replacing the MSE objective with a noise-model aware composite loss function comprising of the Itakura-Saito divergence and a gradient consistency regularizer. This ensures that our approach effectively handles multiplicative interference while preserving the inherent self-supervised nature of Deep Image Prior. The Itakura-Saito divergence is derived as the negative logarithmic likelihood under Gamma-distributed noise. Furthermore, to address the “overfitting to noise” problem inherent in Deep Image Prior, we introduce a patience based automated early stopping strategy to identify the approximate optimal restoration point. Experiments on synthetically corrupted benchmark images show that our approach achieves competitive Peak Signal-to-Noise Ratio and superior Structural Similarity Index Measure compared to Deep Image Prior and representative classical baselines. Notably, our framework achieves these results with a substantial reduction in runtime (average $17.4 \times$ speedup). Finally, we evaluated the reliability of the framework through adversarial stress tests and stochastic initializations, demonstrating that the model remains stable even under intentional signal perturbations.