解决多通道信号测量错位的重建问题，支持更复杂的信号结构。
Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces
- 基于子空间并集建模，处理跨通道测量错位问题。
- 理论推导出更紧的采样下限，确保唯一重构。
- 适用于脑成像等真实场景中样本与通道错配的情况。
跨通道无标签感知旨在从通道间错位的测量中恢复多通道信号。本文将该框架扩展至信号位于子空间并集的情形，可处理更复杂的信号结构，并拓展至压缩感知等任务。此类样本与通道的不匹配常见于自由活动生物的全脑钙成像或多目标追踪。相比先前模型，本文推导出更紧的唯一重构所需采样数量边界，同时支持更一般的信号类型。通过全脑钙成像应用验证：动物运动导致样本与神经元映射失准，本方法仍能实现精确信号重建，证明了其在实际中样本-通道关联不精确场景下的有效性。
原文摘要 · Abstract (English)
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.
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