We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while self-supervised methods allow incomplete ground truth but typically rely on random sampling that, in expectation, covers the entire image. In contrast, we consider fixed, deterministic sampling patterns with inherently incomplete coverage, even in expectation. To overcome this limitation, we exploit multiple invariances of the underlying image distribution, which theoretically allows us to achieve the same reconstruction performance as fully supervised approaches. We validate our method on optical-resolution image upsampling in photoacoustic microscopy (PAM), demonstrating competitive or superior results while requiring substantially less ground truth data.

翻译：我们研究从不完整测量中重建图像的问题，涵盖上采样和图像修复，并基于学习框架展开。传统监督方法需要完整采样的真实数据，而自监督方法虽允许不完整真实数据，但通常依赖随机采样——期望上覆盖全图。与此相对，我们考虑固定、确定性的采样模式，即使在期望意义上也存在固有不完整覆盖。为克服这一限制，我们利用底层图像分布的多种不变性，理论上可实现与完全监督方法相同的重建性能。我们在光声显微成像（PAM）的光学分辨率图像上采样中验证了该方法，在显著减少真实数据需求的同时，展现出具有竞争力或更优的结果。