# Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems

arXiv: https://arxiv.org/abs/1902.09699 · HTML: https://mlsanity.com/paper/1902.09699/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

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

- [ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems](https://mlsanity.com/paper/2405.05398/) (2024)
- [Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators](https://mlsanity.com/paper/2203.14396/) (2022)
- [Learned multiphysics inversion with differentiable programming and machine learning](https://mlsanity.com/paper/2304.05592/) (2023)

## Abstract (arXiv)

We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse problems in physical parameter estimation and image processing. The primary design criterion is working with multiple sets, which allows us to solve inverse problems with multiple pieces of prior knowledge. Our algorithms outperform the well known Dykstra's algorithm when individual sets are not easy to project onto because we exploit similarities between constraint sets. Other design choices that make the software fast and practical to use, include recently developed automatic selection methods for auxiliary algorithm parameters, fine and coarse grained parallelism, and a multilevel acceleration scheme. We provide implementation details and examples that show how the software can be used to regularize inverse problems. Results show that we benefit from working with all available prior information and are not limited to one or two regularizers because of algorithmic, computational, or hyper-parameter selection issues.