Bibliographic Details
| Title: |
Shuffled multi-channel sparse signal recovery. |
| Authors: |
Koka, Taulant1 (AUTHOR) taulant.koka@tu-darmstadt.de, Tsakiris, Manolis C.2 (AUTHOR) manolis@amss.ac.cn, Muma, Michael1 (AUTHOR) michael.muma@tu-darmstadt.de, Béjar Haro, Benjamín3 (AUTHOR) benjamin.bejar@psi.ch |
| Source: |
Signal Processing. Nov2024, Vol. 224, pN.PAG-N.PAG. 1p. |
| Subjects: |
Signal reconstruction, Vital signs, Evaluation methodology, Calcium, Signals & signaling |
| Abstract: |
Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To address this issue systematically, we frame it as a signal reconstruction problem where correspondences between samples and channels are lost. Assuming a sensing matrix for the signals, we show the problem's equivalence to a highly structured unlabeled sensing problem and establish conditions for unique recovery. This is crucial since existing unlabeled sensing theory is inapplicable and results for reconstructing shuffled multi-channel signals do not yet exist. Our results extend to continuous-time sparse signals, and we derive conditions for reconstructing shuffled sparse signals. For the two-channel case, we provide a first reconstruction method, which combines sparse signal recovery with robust linear regression, outperforming existing unlabeled sensing methods in numerical experiments. Additionally, we showcase its effectiveness in a real-world application involving calcium imaging traces. Our theory marks a significant initial step in addressing this challenging signal reconstruction problem, with potential extensions to diverse signal representations encountered in real-world problems with imprecise measurement or channel assignment. • Formalization of the shuffled multi-channel signal reconstruction problem. • Derivation of unique recovery conditions for cross-channel unlabeled sensing problem. • Extension of recovery results to sparse signals with unknown sensing matrix. • Proposal of two-step approach for shuffled sparse signal reconstruction. • Evaluation of the method in simulations and a practical application in neuroscience. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
