Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces
Journal:
arXiv
Published Date:
Jun 11, 2025
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.
