  We propose a general framework for solving inverse problems in the presence
of noise that requires no signal prior, no noise estimate, and no clean
training data. We only require that the forward model be available and that the
noise be statistically independent across measurement dimensions. We build upon
the theory of $\mathcal{J}$-invariant functions (Batson & Royer 2019,
arXiv:1901.11365) and show how self-supervised denoising \emph{\`a la}
Noise2Self is a special case of learning a noise-tolerant pseudo-inverse of the
identity. We demonstrate our approach by showing how a convolutional neural
network can be taught in a self-supervised manner to deconvolve images and
surpass in image quality classical inversion schemes such as Lucy-Richardson
deconvolution.
