Image Deconvolution via Noise-Tolerant Self-Supervised Inversion
This addresses the challenge of solving inverse problems in imaging for applications like microscopy or astronomy, offering a more flexible and data-efficient method, though it builds on existing self-supervised techniques.
The paper tackles the problem of image deconvolution in the presence of noise without requiring signal priors, noise estimates, or clean training data, by proposing a self-supervised framework that learns a noise-tolerant pseudo-inverse, and it demonstrates that this approach surpasses classical methods like Lucy-Richardson deconvolution in image quality.
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{à 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.