# Joint Manifold Learning and Optimal Transport for Dynamic Imaging

arXiv: https://arxiv.org/abs/2505.11913 · HTML: https://mlsanity.com/paper/2505.11913/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 19 of 19)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning](https://mlsanity.com/paper/1708.01955/) (2017)
- [Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning](https://mlsanity.com/paper/2204.06645/) (2022)
- [Wasserstein Patch Prior for Image Superresolution](https://mlsanity.com/paper/2109.12880/) (2021)
- [Barycenters of Natural Images -- Constrained Wasserstein Barycenters for Image Morphing](https://mlsanity.com/paper/1912.11545/) (2019)
- [A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging](https://mlsanity.com/paper/1812.03446/) (2018)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [A Variational Model for Joint Motion Estimation and Image Reconstruction](https://mlsanity.com/paper/1607.03255/) (2016)
- [Manifold learning in Wasserstein space](https://mlsanity.com/paper/2311.08549/) (2023)
- [Image reconstruction in dynamic inverse problems with temporal models](https://mlsanity.com/paper/2007.10238/) (2020)
- [Indirect Image Registration with Large Diffeomorphic Deformations](https://mlsanity.com/paper/1706.04048/) (2017)
- [A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization](https://mlsanity.com/paper/2012.11706/) (2020)
- [Optimal Transport on the Lie Group of Roto-translations](https://mlsanity.com/paper/2402.15322/) (2024)
- [Template-Based Image Reconstruction from Sparse Tomographic Data](https://mlsanity.com/paper/1810.08596/) (2018)
- [Spatiotemporal Imaging with Diffeomorphic Optimal Transportation](https://mlsanity.com/paper/2011.11906/) (2020)
- [Improving Autoencoder Image Interpolation via Dynamic Optimal Transport](https://mlsanity.com/paper/2404.08900/) (2024)
- [Image reconstruction through metamorphosis](https://mlsanity.com/paper/1806.01225/) (2018)
- [Template-Based Image Reconstruction Facing Different Topologies](https://mlsanity.com/paper/2108.13777/) (2021)

## Built on by (most cited first, 1 of 1)

- [RONOM: Reduced-Order Neural Operator Modeling](https://mlsanity.com/paper/2507.12814/) (2025)

## Abstract (arXiv)

Dynamic imaging is critical for understanding and visualizing dynamic biological processes in medicine and cell biology. These applications often encounter the challenge of a limited amount of time series data and time points, which hinders learning meaningful patterns. Regularization methods provide valuable prior knowledge to address this challenge, enabling the extraction of relevant information despite the scarcity of time-series data and time points. In particular, low-dimensionality assumptions on the image manifold address sample scarcity, while time progression models, such as optimal transport (OT), provide priors on image development to mitigate the lack of time points. Existing approaches using low-dimensionality assumptions disregard a temporal prior but leverage information from multiple time series. OT-prior methods, however, incorporate the temporal prior but regularize only individual time series, ignoring information from other time series of the same image modality. In this work, we investigate the effect of integrating a low-dimensionality assumption of the underlying image manifold with an OT regularizer for time-evolving images. In particular, we propose a latent model representation of the underlying image manifold and promote consistency between this representation, the time series data, and the OT prior on the time-evolving images. We discuss the advantages of enriching OT interpolations with latent models and integrating OT priors into latent models.