Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces
This addresses signal recovery challenges in applications like neuroscience imaging and multi-target tracking where sample-channel associations are imprecise, representing an incremental extension of an existing framework.
The paper tackles the problem of recovering multi-channel signals from measurements shuffled across channels by extending the cross-channel unlabeled sensing framework to signals in a union of subspaces, which broadens applicability to tasks like compressed sensing. It improves over previous models by deriving tighter bounds on sample requirements for unique reconstruction and demonstrates utility in whole-brain calcium imaging, achieving accurate signal reconstruction despite disrupted sample-to-neuron mappings.
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.