Semi-supervised Super-resolution for Gravitational Lenses with Estimated Degradation Model

High-resolution lensing images are essential in astrophysics for identifying and studying a range of physical phenomena, in particular the nature of dark matter. Deep learning approaches that learn super-resolution often require large amounts of training data. When the forward model (or degradation process) for super-resolution is known, model-based architectures such as loop unrolling have been shown to provide superior results and are more data-efficient than direct reconstruction methods. The classic loop unrolling requires knowing the forward model precisely, while a recent work addresses errors in forward model by iterative adaptation along reconstruction, achieving high reconstruction quality across various tasks but is designed for supervised learning only. High-resolution gravitational lensing images are expensive to obtain, but numerous low-resolution images are available. We propose to use an $\mathbf{A}$-adaptive loop unrolling architecture for high-resolution reconstruction, and incorporate the untrained adaptively estimated forward model network as part of the semi-supervised training loss. Experimental results demonstrate significant performance gains when leveraging the estimated forward model across different amounts of paired data.