  Ill-posed image reconstruction problems appear in many scenarios such as
remote sensing, where obtaining high quality images is crucial for
environmental monitoring, disaster management and urban planning. Deep learning
has seen great success in overcoming the limitations of traditional methods.
However, these inverse problems rarely come with ground truth data,
highlighting the importance of unsupervised learning from partial and noisy
measurements alone. We propose perspective-equivariant imaging (EI), a
framework that leverages perspective variability in optical camera-based
imaging systems, such as satellites or handheld cameras, to recover information
lost in ill-posed optical camera imaging problems. This extends previous EI
work to include a much richer non-linear class of group transforms and is shown
to be an excellent prior for satellite and urban image data, where
perspective-EI achieves state-of-the-art results in multispectral
pansharpening, outperforming other unsupervised methods in the literature. Code
at https://andrewwango.github.io/perspective-equivariant-imaging
