# Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport

arXiv: https://arxiv.org/abs/1612.02273 · HTML: https://mlsanity.com/paper/1612.02273/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2016.

## Built on by (most cited first, 7 of 7)

- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Toric Geometry of Entropic Regularization](https://mlsanity.com/paper/2202.01571/) (2022)
- [Proximal Mean Field Learning in Shallow Neural Networks](https://mlsanity.com/paper/2210.13879/) (2022)
- [A Distributed Algorithm for Measure-valued Optimization with Additive Objective](https://mlsanity.com/paper/2202.08930/) (2022)
- [A Relaxed Wasserstein Distance Formulation for Mixtures of Radially Contoured Distributions](https://mlsanity.com/paper/2503.13893/) (2025)
- [Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization](https://mlsanity.com/paper/2509.10693/) (2025)
- [Coupled Optimal Transport with Landmark Constraints](https://mlsanity.com/paper/2608.19783/) (2026)

## Abstract (arXiv)

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be formulated as a linear programming problem, it is in many cases intractable for large problems due to the vast number of variables. A recent development to address this builds on an approximation with an entropic barrier term and solves the resulting optimization problem using Sinkhorn iterations. In this work we extend this methodology to a class of inverse problems. In particular we show that Sinkhorn-type iterations can be used to compute the proximal operator of the transport problem for large problems. A splitting framework is then used to solve inverse problems where the optimal mass transport cost is used for incorporating a priori information. We illustrate the method on problems in computerized tomography. In particular we consider a limited-angle computerized tomography problem, where a priori information is used to compensate for missing measurements.