# Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces

arXiv: https://arxiv.org/abs/2506.09773 · HTML: https://mlsanity.com/paper/2506.09773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Linear Regression with Sparsely Permuted Data](https://mlsanity.com/paper/1710.06030/) (2017)
- [Linear regression without correspondence](https://mlsanity.com/paper/1705.07048/) (2017)
- [Linear Regression with Shuffled Labels](https://mlsanity.com/paper/1705.01342/) (2017)
- [Linear Regression without Correspondences via Concave Minimization](https://mlsanity.com/paper/2003.07706/) (2020)
- [A Pseudo-Likelihood Approach to Linear Regression with Partially Shuffled Data](https://mlsanity.com/paper/1910.01623/) (2019)
- [Permutations Unlabeled beyond Sampling Unknown](https://mlsanity.com/paper/1812.00498/) (2018)
- [Uncoupled Regression from Pairwise Comparison Data](https://mlsanity.com/paper/1905.13659/) (2019)
- [Unlabeled Principal Component Analysis and Matrix Completion](https://mlsanity.com/paper/2101.09446/) (2021)
- [r-local sensing: Improved algorithm and applications](https://mlsanity.com/paper/2110.14034/) (2021)
- [R-local unlabeled sensing: A novel graph matching approach for multiview unlabeled sensing under local permutations](https://mlsanity.com/paper/1911.06382/) (2019)
- [Estimation in exponential family Regression based on linked data contaminated by mismatch error](https://mlsanity.com/paper/2010.00181/) (2020)
- [Shuffled linear regression through graduated convex relaxation](https://mlsanity.com/paper/2209.15608/) (2022)
- [Shuffled Multi-Channel Sparse Signal Recovery](https://mlsanity.com/paper/2212.07368/) (2022)

## Abstract (arXiv)

Cross-channel unlabeled sensing addresses the problem of recovering a multi-channel signal from measurements that were shuffled across channels. This work expands the cross-channel unlabeled sensing framework to signals that lie in a union of subspaces. The extension allows for handling more complex signal structures and broadens the framework to tasks like compressed sensing. These mismatches between samples and channels often arise in applications such as whole-brain calcium imaging of freely moving organisms or multi-target tracking. We improve over previous models by deriving tighter bounds on the required number of samples for unique reconstruction, while supporting more general signal types. The approach is validated through an application in whole-brain calcium imaging, where organism movements disrupt sample-to-neuron mappings. This demonstrates the utility of our framework in real-world settings with imprecise sample-channel associations, achieving accurate signal reconstruction.