Joint Manifold Learning and Optimal Transport for Dynamic Imaging

TL;DR

This paper introduces a novel approach combining low-dimensional manifold assumptions with optimal transport priors to improve dynamic imaging analysis, especially when data is scarce, by promoting consistency between latent representations and observed data.

Contribution

It proposes a latent model framework that integrates manifold learning with optimal transport priors, enhancing the analysis of time-evolving images with limited data.

Findings

Enriched OT interpolations with latent models improve image reconstruction.

Integrating OT priors into latent models enhances temporal consistency.

The method effectively handles data scarcity in dynamic imaging.

Abstract

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.