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

arXiv: https://arxiv.org/abs/2503.19468 · HTML: https://mlsanity.com/paper/2503.19468/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise](https://mlsanity.com/paper/2205.10278/) (2022)
- [UNSURE: self-supervised learning with Unknown Noise level and Stein's Unbiased Risk Estimate](https://mlsanity.com/paper/2409.01985/) (2024)
- [Cryo-CARE: Content-Aware Image Restoration for Cryo-Transmission Electron Microscopy Data](https://mlsanity.com/paper/1810.05420/) (2018)
- [Clean self-supervised MRI reconstruction from noisy, sub-sampled training data with Robust SSDU](https://mlsanity.com/paper/2210.01696/) (2022)
- [Sparse2Inverse: Self-supervised inversion of sparse-view CT data](https://mlsanity.com/paper/2402.16921/) (2024)
- [A Deep Learning Method for Simultaneous Denoising and Missing Wedge Reconstruction in Cryogenic Electron Tomography](https://mlsanity.com/paper/2311.05539/) (2023)
- [Regularization of Inverse Problems by Neural Networks](https://mlsanity.com/paper/2006.03972/) (2020)
- [Self-Supervised Learning for Improved Calibrationless Radial MRI with NLINV-Net](https://mlsanity.com/paper/2402.06550/) (2024)

## Built on by (most cited first, 5 of 5)

- [HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training](https://mlsanity.com/paper/2601.01228/) (2026)
- [SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography](https://mlsanity.com/paper/2604.15651/) (2026)
- [Self-Supervised Angular Deblurring in Photoacoustic Reconstruction via Noisier2Inverse](https://mlsanity.com/paper/2604.15681/) (2026)
- [Enabling self-supervised learned primal dual with Noise2Inverse](https://mlsanity.com/paper/2606.26991/) (2026)
- [Denoising ICF Images with Multiplicative Uniform Noise: A Self-Supervised Study Based on the Log-Domain Noisier2Inverse Framework](https://mlsanity.com/paper/2606.27635/) (2026)

## Abstract (arXiv)

We propose Noisier2Inverse, a correction-free self-supervised deep learning approach for general inverse problems. The proposed method learns a reconstruction function without the need for ground truth samples and is applicable in cases where measurement noise is statistically correlated. This includes computed tomography, where detector imperfections or photon scattering create correlated noise patterns, as well as microscopy and seismic imaging, where physical interactions during measurement introduce dependencies in the noise structure. Similar to Noisier2Noise, a key step in our approach is the generation of noisier data from which the reconstruction network learns. However, unlike Noisier2Noise, the proposed loss function operates in measurement space and is trained to recover an extrapolated image instead of the original noisy one. This eliminates the need for an extrapolation step during inference, which would otherwise suffer from ill-posedness. We numerically demonstrate that our method clearly outperforms previous self-supervised approaches that account for correlated noise.