# Equivariance-based self-supervised learning for audio signal recovery from clipped measurements

arXiv: https://arxiv.org/abs/2409.15283 · HTML: https://mlsanity.com/paper/2409.15283/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 9 of 9)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [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)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [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)
- [Sparsity-based audio declipping methods: selected overview, new algorithms, and large-scale evaluation](https://mlsanity.com/paper/2005.10228/) (2020)
- [Consistent Iterative Hard Thresholding For Signal Declipping](https://mlsanity.com/paper/1303.1023/) (2013)

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

- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [Equivariant Splitting: Self-supervised learning from incomplete data](https://mlsanity.com/paper/2510.00929/) (2025)
- [Self-supervised learning for phase retrieval](https://mlsanity.com/paper/2509.26203/) (2025)
- [Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imaging](https://mlsanity.com/paper/2601.23037/) (2026)
- [Learning to reconstruct from saturated data: audio declipping and high-dynamic range imaging](https://mlsanity.com/paper/2602.22279/) (2026)

## Abstract (arXiv)

In numerous inverse problems, state-of-the-art solving strategies involve training neural networks from ground truth and associated measurement datasets that, however, may be expensive or impossible to collect. Recently, self-supervised learning techniques have emerged, with the major advantage of no longer requiring ground truth data. Most theoretical and experimental results on self-supervised learning focus on linear inverse problems. The present work aims to study self-supervised learning for the non-linear inverse problem of recovering audio signals from clipped measurements. An equivariance-based selfsupervised loss is proposed and studied. Performance is assessed on simulated clipped measurements with controlled and varied levels of clipping, and further reported on standard real music signals. We show that the performance of the proposed equivariance-based self-supervised declipping strategy compares favorably to fully supervised learning while only requiring clipped measurements alone for training.