# Inverse Problems in Topological Persistence

arXiv: https://arxiv.org/abs/1810.10813 · HTML: https://mlsanity.com/paper/1810.10813/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2018.

## Built on by (most cited first, 5 of 5)

- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)
- [From Geometry to Topology: Inverse Theorems for Distributed Persistence](https://mlsanity.com/paper/2101.12288/) (2021)
- [Optimisation of Spectral Wavelets for Persistence-based Graph Classification](https://mlsanity.com/paper/2101.05201/) (2021)
- [Reconstruction of univariate functions from directional persistence diagrams](https://mlsanity.com/paper/2203.01894/) (2022)
- [Convolutional Persistence Transforms](https://mlsanity.com/paper/2208.02107/) (2022)

## Abstract (arXiv)

In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. the existence of right inverses, and the second half focuses on injectivity, i.e. left inverses. Throughout, we highlight the tools and theorems that underlie these advances, and direct the reader's attention to open problems, both theoretical and applied.