# Inverse Problems with Invariant Multiscale Statistics

arXiv: https://arxiv.org/abs/1609.05502 · HTML: https://mlsanity.com/paper/1609.05502/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2016.

## Built on by (most cited first, 3 of 3)

- [Learned Interferometric Imaging for the SPIDER Instrument](https://mlsanity.com/paper/2301.10260/) (2023)
- [CXR-Net: An Artificial Intelligence Pipeline for Quick Covid-19 Screening of Chest X-Rays](https://mlsanity.com/paper/2103.00087/) (2021)
- [Synergizing Deep Learning and Full-Waveform Inversion: Bridging Data-Driven and Theory-Guided Approaches for Enhanced Seismic Imaging](https://mlsanity.com/paper/2502.17585/) (2025)

## Abstract (arXiv)

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale scattering transform which discards the phase and thus exposes strong spectral correlations otherwise hidden beneath the phase fluctuations. As a result, both constraints may be put into effect by linear projections in their respective spaces. We apply the algorithm to super-resolution and tomography and show that it outperforms ad hoc convex regularizers and stably recovers the missing spectrum.