# 3D unknown view tomography via rotation invariants

arXiv: https://arxiv.org/abs/2003.10107 · HTML: https://mlsanity.com/paper/2003.10107/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors](https://mlsanity.com/paper/2309.09032/) (2023)
- [Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography](https://mlsanity.com/paper/2207.02985/) (2022)
- [An Adversarial Learning Based Approach for Unknown View Tomographic Reconstruction](https://mlsanity.com/paper/2108.09873/) (2021)
- [Phase retrieval with rank d measurements -- descending algorithms phase transitions](https://mlsanity.com/paper/2506.18282/) (2025)

## Abstract (arXiv)

In this paper, we study the problem of reconstructing a 3D point source model from a set of 2D projections at unknown view angles. Our method obviates the need to recover the projection angles by extracting a set of rotation-invariant features from the noisy projection data. From the features, we reconstruct the density map through a constrained nonconvex optimization. We show that the features have geometric interpretations in the form of radial and pairwise distances of the model. We further perform an ablation study to examine the effect of various parameters on the quality of the estimated features from the projection data. Our results showcase the potential of the proposed method in reconstructing point source models in various noise regimes.