Reconstruction of Multivariate Sparse Signals from Mismatched Samples

by Taulant Koka (TU Darmstadt)

Wednesday 16 Nov 2022, 11:30 → 13:00 Europe/Zurich

https://psich.zoom.us/j/69987529439?pwd=K0o4ZU9SZEQ0c2xnbU5IaTMranU5UT09 Meeting-ID: 699 8752 9439 Kenncode: 260808 (OHSA/B17)

Abstract: Erroneous correspondences between samples and their respective channel or target is a type of corruption that commonly arises in several real-world applications, such as whole-brain calcium imaging of freely moving organisms, the observation of insect flight and migration based on entomological radar, or multi-target tracking. We formalize the problem of reconstructing shuffled multi-channel signals that admit a sparse representation in a continuous domain and show that unique recovery is possible. We show that the problem is equivalent to a structured unlabeled sensing problem with sensing matrix estimation. Unfortunately, existing methods are neither robust to errors in the regressors nor do they exploit the structure of the problem. Therefore, we propose a novel robust two-step approach for the reconstruction of shuffled sparse signals. The proposed approach is evaluated on both synthetic and artificially shuffled real calcium imaging traces showing a significant performance gain as compared to existing methods.