Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise

We propose Noisier2Inverse, a correction-free, self-supervised deep learning method for general inverse problems. Our approach learns a reconstruction function without requiring ground truth data and is applicable in settings where measurement noise is statistically correlated. This includes applications such as computed tomography, where detector imperfections and photon scattering induce structured noise, as well as microscopy and seismic imaging, where physical interactions during acquisition lead to noise dependencies. Like Noisier2Noise, our method relies on generating noisier inputs to guide training via a network operating in image space. However, in contrast to Noisier2Noise, the loss function in Noisier2Inverse is defined in the measurement space and targets the recovery of an extrapolated image rather than the original noisy one. This design avoids the need for an explicit extrapolation step during inference, which would otherwise be affected by the ill-posedness of the inverse problem. We provide numerical evidence that Noisier2Inverse outperforms prior self-supervised methods designed to handle correlated noise. This indicates that Noisier2Inverse fills a gap in current self-supervised image reconstruction methods for correlated noise.