# Shuffled Multi-Channel Sparse Signal Recovery

arXiv: https://arxiv.org/abs/2212.07368 · HTML: https://mlsanity.com/paper/2212.07368/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 63 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Multi-Task Temporal Shift Attention Networks for On-Device Contactless Vitals Measurement](https://mlsanity.com/paper/2006.03790/) (2020)
- [Linear Regression with Sparsely Permuted Data](https://mlsanity.com/paper/1710.06030/) (2017)
- [Linear regression without correspondence](https://mlsanity.com/paper/1705.07048/) (2017)
- [Linear Regression with Shuffled Labels](https://mlsanity.com/paper/1705.01342/) (2017)
- [Linear Regression without Correspondences via Concave Minimization](https://mlsanity.com/paper/2003.07706/) (2020)
- [Signal Recovery from Unlabeled Samples](https://mlsanity.com/paper/1701.08701/) (2017)
- [A Pseudo-Likelihood Approach to Linear Regression with Partially Shuffled Data](https://mlsanity.com/paper/1910.01623/) (2019)
- [Permutations Unlabeled beyond Sampling Unknown](https://mlsanity.com/paper/1812.00498/) (2018)
- [Uncoupled Regression from Pairwise Comparison Data](https://mlsanity.com/paper/1905.13659/) (2019)
- [Unlabeled Principal Component Analysis and Matrix Completion](https://mlsanity.com/paper/2101.09446/) (2021)
- [r-local sensing: Improved algorithm and applications](https://mlsanity.com/paper/2110.14034/) (2021)
- [R-local unlabeled sensing: A novel graph matching approach for multiview unlabeled sensing under local permutations](https://mlsanity.com/paper/1911.06382/) (2019)
- [Estimation in exponential family Regression based on linked data contaminated by mismatch error](https://mlsanity.com/paper/2010.00181/) (2020)
- [When do wireless network signals appear Poisson?](https://mlsanity.com/paper/1411.3757/) (2014)
- [Homomorphic Sensing of Subspace Arrangements](https://mlsanity.com/paper/2006.05158/) (2020)
- [Shuffled linear regression through graduated convex relaxation](https://mlsanity.com/paper/2209.15608/) (2022)
- [CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI](https://mlsanity.com/paper/2006.06374/) (2020)

## Built on by (most cited first, 1 of 1)

- [Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces](https://mlsanity.com/paper/2506.09773/) (2025)

## Abstract (arXiv)

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 systematically address this fundamental problem, we pose it as a signal reconstruction problem where we have lost correspondences between the samples and their respective channels. Assuming that we have a sensing matrix for the underlying signals, we show that the problem is equivalent to a structured unlabeled sensing problem, and establish sufficient conditions for unique recovery. To the best of our knowledge, a sampling result for the reconstruction of shuffled multi-channel signals has not been considered in the literature and existing methods for unlabeled sensing cannot be directly applied. We extend our results to the case where the signals admit a sparse representation in an overcomplete dictionary (i.e., the sensing matrix is not precisely known), and derive sufficient conditions for the reconstruction of shuffled sparse signals. We propose a robust reconstruction method that combines sparse signal recovery with robust linear regression for the two-channel case. The performance and robustness of the proposed approach is illustrated in an application related to whole-brain calcium imaging. The proposed methodology can be generalized to sparse signal representations other than the ones considered in this work to be applied in a variety of real-world problems with imprecise measurement or channel assignment.