Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces

TL;DR

This paper extends cross-channel unlabeled sensing to signals in a union of subspaces, enabling better handling of complex structures and real-world applications like calcium imaging with moving organisms.

Contribution

It introduces a union of subspaces model into unlabeled sensing, providing tighter bounds and supporting more complex signal types than previous models.

Findings

Tighter bounds on sample requirements for unique reconstruction.

Successful application to whole-brain calcium imaging with organism movement.

Demonstrated robustness in real-world noisy, mismatched sample-channel scenarios.

Abstract

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.