# Learning to reconstruct from saturated data: audio declipping and high-dynamic range imaging

arXiv: https://arxiv.org/abs/2602.22279 · HTML: https://mlsanity.com/paper/2602.22279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Enabling Factorized Piano Music Modeling and Generation with the MAESTRO Dataset](https://mlsanity.com/paper/1810.12247/) (2018)
- [HDR image reconstruction from a single exposure using deep CNNs](https://mlsanity.com/paper/1710.07480/) (2017)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Solving Audio Inverse Problems with a Diffusion Model](https://mlsanity.com/paper/2210.15228/) (2022)
- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [Exact and Stable Covariance Estimation from Quadratic Sampling via Convex Programming](https://mlsanity.com/paper/1310.0807/) (2013)
- [Single-Image HDR Reconstruction by Multi-Exposure Generation](https://mlsanity.com/paper/2210.15897/) (2022)
- [Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurring](https://mlsanity.com/paper/2312.11232/) (2023)
- [A survey and an extensive evaluation of popular audio declipping methods](https://mlsanity.com/paper/2007.07663/) (2020)
- [Learning to Reconstruct Signals From Binary Measurements](https://mlsanity.com/paper/2303.08691/) (2023)
- [Equivariance-based self-supervised learning for audio signal recovery from clipped measurements](https://mlsanity.com/paper/2409.15283/) (2024)
- [Perceptual Region-Driven Infrared-Visible Co-Fusion for Extreme Scene Enhancement](https://mlsanity.com/paper/2512.06400/) (2025)
- [Sparsity-based audio declipping methods: selected overview, new algorithms, and large-scale evaluation](https://mlsanity.com/paper/2005.10228/) (2020)
- [High Dynamic Range Modulo Imaging for Robust Object Detection in Autonomous Driving](https://mlsanity.com/paper/2504.11472/) (2025)
- [Consistent Iterative Hard Thresholding For Signal Declipping](https://mlsanity.com/paper/1303.1023/) (2013)

## Abstract (arXiv)

Learning based methods are now ubiquitous for solving inverse problems, but their deployment in real-world applications is often hindered by the lack of ground truth references for training. Recent self-supervised learning strategies offer a promising alternative, avoiding the need for ground truth. However, most existing methods are limited to linear inverse problems. This work extends self-supervised learning to the non-linear problem of recovering audio and images from clipped measurements, by assuming that the signal distribution is approximately invariant to changes in amplitude. We provide sufficient conditions for learning to reconstruct from saturated signals alone and a self-supervised loss that can be used to train reconstruction networks. Experiments on both audio and image data show that the proposed approach is almost as effective as fully supervised approaches, despite relying solely on clipped measurements for training.