Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces
🤖 AI Summary
This work addresses signal aliasing and channel misalignment in cross-channel unlabeled sensing—where multichannel measurements are shuffled, causing reconstruction mismatch, and the underlying signal lies in a union of subspaces, a highly structured non-convex domain. We propose the first unlabeled sensing framework tailored to the union-of-subspaces (UoS) model. Methodologically, we integrate subspace clustering, non-convex optimization, and geometric analysis with compressed sensing theory and explicit channel misalignment modeling, rigorously deriving a tighter sufficient condition on the minimum number of measurements for unique recovery. Unlike conventional labeled or single-subspace assumptions, our framework accommodates broader signal classes and significantly enhances modeling capacity for structurally complex signals. In whole-brain calcium imaging experiments under motion artifacts, it achieves high-fidelity, robust neural activity reconstruction, empirically validating its effectiveness and practicality in realistic misalignment scenarios.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Recovering multi-channel signals from shuffled measurements
Extending framework to signals in union of subspaces
Improving sample bounds for unique reconstruction
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extends unlabeled sensing to union of subspaces
Derives tighter bounds for unique reconstruction
Validates with whole-brain calcium imaging
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